.-ORES,iiii| 
MENSURATIOl 



HERMAN H. CHAPMAN 



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GopightN®_ 



CORfRIGHT DEPOSrr. 



FOREST MENSURATION 



BY 

HERMAN HAUPT CHAPMAN, M.F. 

Harriman Professor of Forest Management, 
Yale University 



NEW YORK 

JOHN WILEY & SONS, Inc. 

London: CHAPMAN & HALL, Limited 
1921 



5J! 



s5\ 



Copyright, 1921 
By HERMAN HAUPT CHAPMAN 




OCT -7 7 



PRESS or 

BRAUNWORTH & CO. 

BOOK MANUFACTURERS 

BROOKLYN, N. Y. 



g)CI.A624703 



i X 



TO 

IN RECOGNITION OF HIS LIFELONG SERVICE 

IN PROMOTING FOREST EDUCATION 

AND IN DEVELOPING A HIGH STANDARD 

OF PROFESSIONAL FORESTRY IN AMERICA 



PREFACE 



This text is intended as a thorough discussion of the measurement 
of the volume of felled timber, in the form of logs or other products; 
of the measurement of the volume of standing timber; and of the 
growth of trees, stands of timber and forests. It is designed for the 
information of students of forestry, owners or purchasers of timber- 
lands, and timber operators. The subject matter so treated is funda- 
mental to the purchase or exchange of forest property or of timber 
stumpage, the valuation of damages, the planning of logging operations, 
and the management of forest lands for the production of timber by 
growth. 

The publication is intended as the successor of Graves' Forest Men- 
suration, and was undertaken at the request of the author, H. S. Graves, 
whose original text, Forest Mensuration, appearing in 1906, set a stand- 
ard for text-books in forestry and has been of inestimable value to 
foresters and timberland owners in America. The present text is not a 
revision of the former publication, but an entirely new presentation, 
both as to arrangement, methods of treatment and much of the subject 
matter. The author has in some instances quoted or borrowed portions 
of the former text and is indebted to it for many of the more fundamental 
conceptions and descriptions of processes used in Forest Mensuration. 

It is the purpose of Part I to bring out the relations of the cubic 
contents of logs, and their measurement, to the contents as expressed in 
terms of products, and to encourage the substitution of sound units of 
measure and methods of measurement for defective standards and 
methods as far as possible. 

The application of these standards to the measurement of standing 
timber is the subject of Part II. This part presents a complete analysis 
of the art of timber estimating as practiced in every timber region of the 
United States, the methods employed by skilled timber cruisers, the 
principles upon which these methods are based, the relative accuracy 
of the various systems used, the factors and averages which enter into 
the use of these methods, and the application of these principles and 
factors in practical work and in the training of men for timber cruising. 



vi PREFACE 

The object sought in Part III is to systematize the principles and 
problems confronting the student in the, study of tree growtlt, and to so 
correlate these problems that he is not diverted from the ultimate object 
of such/< studies, which is the determination of yields per acre, by details 
of methods having to do with the measurement of growth of individual 
trees. Research and field studies of growth per acre are rendered dif- 
ficult not only by the lack of an accepted unit of measure, but by the 
great variations in the character of the stands comprising our virgin 
and second growth forests, yet it is just these stands, and not planta- 
tions, whose growth will determine our yields of timber for the next 
four or five decades. 

Attention is called to the substitution of the International |-inch 
kerf log rule in the present volume, for the |-inch kerf rule in 
Graves' Mensuration. It is hoped that this rule will be accepted as a 
scientific standard for board feet since it is adapted to conditions of 
second growth and is conservative in values. 

Instead of attempting to include tables of volume or yield, a table 
of references is printed to such tables as are of standard quality and 
which are in possession of the U. S. Forest Service, Washington, D. C. 

The author wishes to acknowledge the many helpful criticisms 
received from foresters in the preparation of this book. 



TABLE OF CONTENTS 



Part I 

THE MEASUREMENT OF FELLED TIMBER AND ITS 

PRODUCTS 

CHAPTER I 
INTRODUCTION TO FOREST MENSURATION 

PAGE 

1. Definition and Purpose 1 

2. Relation between Lumbering and Timber Estimating 2 

3. Relation between Forestry and Growth Measurements 2 

4. Relation between Forest Mensuration, Stumpage Values and the Valuation 

of Forest Property 3 

5. Relation of Mensuration to other Forestry Subjects 3 

6. Absolute versus Relative Accuracy in Mensuration 3 

7. Forest Survey 5 

CHAPTER II 
SYSTEMS AND UNITS OF MEASUREMENT 

8. Systems of Measurement used in Forest Mensuration 6 

9. Piece Measure 7 

10. Cord Measure 7 

11. Cubic Measure 8 

12. Board Measure 8 

13. Log Rules 8 

14. Measurement of Standing Timber Postponed till after Manufacture 8 

15. Measurement of Standing Timber Postponed till after Logging 9 

16. Measurement of Standing Timber in 'the Tree 9 

17. Need of Standardization for both Commercial and Scientific Measurements. 10 

18. Forms of Products into which the Contents of Trees are Converted 11 

19. The Factor of Waste in Manufacture 13 

20. Actual versus Superficial Contents of Sawed Lumber 13 

21. Round-edged Lumber 14 

22. Products made from Bolts and Billets 14 

CHAPTER III 
THE MEASUREMENT OF LOGS. CUBIC CONTENTS 

23. Total versus Merchantable Contents 16 

24. Log Lengths 16 

25. Diameters and Areas of Cross Sections 17 

vii 



viii TABLE OF CONTENTS 

PAGE 

26. The Form of Logs 18 

27. Formulse for Solid Contents of Logs 19 

28. Relative Accuracy of the Smalian and Huber Formulse 21 

29. The Technique of Measuring Logs 22 

30. Girth as a Substitute for Diameter in Log Measurements 24 

CHAPTER IV 
LOG RULES BASED ON CUBIC CONTENTS 

31. Comparison of Log Rules Based on Diameter at Middle and at Small End 

of Log 26 

32. Log Rules in Use, Based on Cubic Volume 28 

33. The Blodgett or New Hampshire Cubic Foot 30 

34. Use of Cubic Foot in Log Scaling 31 

35. Log Rules for Cubic Contents of Squared Timbers 33 

36. Log Rules Expressed in Board-feet but Based Directly upon Cubic Contents 34 

37. Formula for Board-foot Rules Based on Cubic Contents 35 

38. Comparison of Scaled Cubic Contents by Different Log Rules 36 

39. Relation between Cubic Measure and True Board-foot Log Rules 39 

CHAPTER V 
THE MEASUREMENT OF LOGS. BOARD-FOOT CONTENTS 

40. Necessity for Board-foot Log Rules 40 

41. Relation of Diameter of Log to per cent of Utilization in Sawed Lumber ... 40 

42. Errors in Use of Cubic Rules for Board-feet 42 

43. Taper as a Factor in Limiting the Scaling Length of Logs for Board-foot 

Contents 43 

44. The Introduction of Taper into Log Rules 44 

45. Middle Diameter as a Basis for Board-foot Contents 46 

46. Definition and Basis of Over-run 46 

47. Influences Affecting Over-run. The Log Rule Itself 47 

48. Influences Affecting Over-run. Methods of Manufacture 47 

49. Standardization of Variables in Construction of a Log Rule 49 

50. The Need for More Accurate Log Rules 50 

51. The Waste from Slabs and Edgings 50 

62. The Waste from Crook or Sweep 51 

53. The Waste from Saw Kerf 53 

54. Total Per Cent of Waste in a Log 55 

CHAPTER VI 

THE CONSTRUCTION OF LOG RULES FOR BOARD-FOOT 
CONTENTS 

55. Methods Used in Constructing Log Rules for Board-feet 58 

56. The Construction of Rules Based on Mathematical Formulse 59 

57. Comparison of Log Rules Based on Formulse 61 

58. McKenzie Log Rule 63 

69. International Log Rule for f " Kerf, Judson F. Clark, 1900 63 



TABLE OF CONTENTS ix 

PAGE 

60. International Log Rule for i" K^rf, Judson F. Clark, 1917 64 

61. British Columbia Log Rule, 1902 64 

62. Other Formula Rules, Approximately Accurate Both in Principles and 

Quantities 65 

63. Tiemann Log Rule, H. D. Tiemann, 1910 67 

64. Formula Rules Inaccurately Constructed. Baxter Log Rule 67 

65. Doyle Log Rule 68 

66. Effect of Errors in Doyle Rule upon Scaling and Over-run 70 

67. The Construction of Log Rules Based on Diagrams 72 

68. Scribner Log Rule, 1846 73 

69. Spaulding Log Rule, 1868 75 

70. Maine or Holland Rule, 1856 76 

71. Canadian Log Rules 76 

72. Hybrid Log Rules 76 

73. General Formulae for all Log Rules 77 

74. The Construction of Log Rules from Mill Tallies. Graded Log Rules 78 

75. The Massachusetts Log Rule for Round-edged Lumber 79 

76. Conversion of Values of a Standard Rule to Apply to Different Widths of 

Saw Kerf and Thicknesses of Lumber 

77. Limitations to Conversion of Board-foot Log Rules 83 

78. Choice of a Board- foot Log Rule for a Universal Standard 84 

79. Unused and Obsolete Log Rules 85 

CHAPTER VII 
LOG SCALING FOR BOARD MEASURE 

80. The Log Scale 88 

81. The Cylinder as the Standard of Scaling .■ 90 

82. Deductions from Sound Scale, versus Over-run 90 

83. Scaling Practice Based on Measurement of Diameter at Small End of Log 91 

84. Scaling Practice Based on Measurement of Diameter at Middle of Log, or 

Caliper Scale 97 

85. Scale Records 98 

86. The Determination of What Constitutes a Merchantable Log 99 

87. Grades of Lumber and Log Grades 103 

CHAPTER VIII 
THE SCALING OF DEFECTIVE LOGS 

88. Deductions from Scale for Unsound Defects 105 

89. Methods of Making Deductions 105 

90. Effect of Minimum Dimensions of Merchantable Boards upon these Deduc- 

tions 107 

91. Interior Defects 108 

92. Exterior Defects 113 

93. Crook or Sweep 116 

94. Check Scaling 117 

95. Scaling from the Stump 118 

96. The Scaler. . . . , . , , 119 



X TABLE OF CONTENTS 

CHAPTER IX 
STACKED OR CORD MEASURE 

PAGE 

97. Stacked Measure as a Substitute for Cubic Measure 121 

98. The Standard Cord versus Short Cords and Long Cords 121 

99. Measurement of Stacked Wood Cut for Special Purposes 122 

100. Effect of Seasoning on Volume of Stacked Wood 123 

101. Methods of Measurement of Cordwood 123 

102. Solid Cubic Contents of Stacked Wood 124 

103. Effect of Irregular Piling on Solid Contents 124 

104. Effect of Variation in Form of Sticks on Solid Contents 125 

105. Effect of Dimensions of Stick on Solid Contents 126 

106. The Basis for Cordwood Converting Factors 127 

107. Standard Cordwood Converting Factors 128 

108. Converting Factors for Sticks of Different Lengths 128 

109. Converting Factors for Sticks of Different Diameters 129 

110. The Measurement of Solid Contents of Stacked Cords. Xylometers 132 

111. Cordwood Log Rules. The Humphrey Caliper Rule 132 

112. Discounting for Defect in Cord Measure 133 

113. The Measurement of Bark 134 

114. Factors for Converting Stacked Cords to Board Feet 135 

115. Weight as a Measure of Cordwood 137 

Part II 

THE MEASUREMENT OF STANDING TIMBER 

CHAPTER X 

UNITS OF MEASUREMENT FOR STANDING TIMBER 

116. Board Feet — Basis of AppHcation 139 

117. The Piece 140 

118. Choice of Units in Estimating Timber 140 

119. The Log as the Unit in Estimating 140 

120. Log Run, or Average Log Method 143 

121. The Tree as a Unit in Estimating. Volume Tables 144 

122. Volume Tables Based on Standard Taper per Log. "Universal" Volume 

Tables 144 

123. Substitution of Mill Factor for Log Rules in Universal Tables 146 

124. Volume Tables Based on Actual Volumes of Trees 147 

125. The Point of Measurement of Diameters in Volume Tables 148 

126. Bark as Affecting Diameter in Volume Tables 150 

127. Classification of Trees by Diameter 151 

128. Classification of Trees by Height 151 

129. Diameter Alone, versus Diameter and Height, as Basis of Volume Tables ... 152 

130. Standard versus Local Volume Tables 153 

CHAPTER XI 

THE CONSTRUCTION OF STANDARD VOLUME TABLES 
FOR TOTAL CUBIC CONTENTS 

131. Steps in Construction of a Standard Volume Table 154 

132. Selection of Trees for Measurement 154 



TABLE OF CONTENTS xi 

PAGE 

133. The Tree Record 155 

134. Measurements of the Tree Required for Classification 156 

135. Measurement Required to Obtain the Volume of the Tree. Systems Used 158 

136. Computation of Volume of the Tree 161 

137. Classification and Averaging of Tree Volumes According to Diameter and 

Height Classes 163 

138. The Graphic Plotting of Data — Its Advantages 166 

139. Application of Graphic Method in Consti-ucting Volume Tables 169 

140. Harmonized Curves for Standard Volume Tables, Based on Diameter. . . . 169 

141. Harmonized Curves Based on Height 170 

142. Local Volume Tables, Their Construction and Use 174 

143. The Derivation of Local Volume Tables from Standard Tables 175 

144. Volume Tables for Peeled or Solid Wood Contents 176 



CHAPTER XII 

STANDARD VOLUME TABLES FOR MERCHANTABLE 
CUBIC VOLUME AND CORDS 

145. Purpose and Derivation of Tables for Cubic Volume of Trees 177 

146. Branchwood or Lapwood 177 

147. Merchantable Limit in Tops and at D.B.H 177 

148. Stump Heights 178 

149. Merchantable versus Used Length 178 

150. Waste, Definition and Measurement 179 

151. Defect or Cull 179 

152. Conversion of Volume Tables for Cubic Feet to Cords 180 



CHAPTER XIII 
VOLUME TABLES FOR BOARD FEET 

153. The Standard or Basis for Board-foot Volume Tables 182 

154. Adoption of a Standard Log Length 182 

155. Top Diameters, Fixed or Variable Limits 183 

156. Defective Trees, Measurement 184 

157. Total versus Merchantable Heights as a Basis for Tree Classes 185 

158. The Coordination of Merchantable Heights with Top Diameters 185 

159. Construction of Board-foot Volume Tables 188 

160. Data Which Should Accompany a Volume Table 188 

161. Checking the Accuracy of Volume Tables 189 

CHAPTER XIV 

VOLUME TABLES FOR PIECE PRODUCTS, COMBINATION 
AND GRADED VOLUME TABLES 

162. Volume Tables for Piece Products 191 

163. Volume Tables for Railroad Cross Ties 191 

164. Combination Volume Tables for Two or More Products 193 

165. Graded Volume Tables 193 



xii TABLE OF CONTENTS 

CHAPTER XV 
THE FORM OF TREES AND TAPER TABLES 

PAGE 

166. Form as a Third Factor Affecting Volume : 196 

167. Taper Tables, Definition and Purpose 197 

168. Methods of Constructing Taper Tables 197 

169. Limitations of Taper Tables 204 

CHAPTER XVI 
FORM CLASSES AND FORM FACTORS 

170. The Need for Form Classes in Volume Tables 205 

171. Form Quotient as the Basis of Form Classes 206 

172. Resistance to Wind Pressure as the Determining Factor of Tree Form. . . . 208 

173. A General Formula for Tree Form 209 

174. Applicability of Hoejer's Formula in Determining Tree Forms 210 

175. Form P'actors 211 

176. The Derivation of Standard Breast High Form Factors 213 

177. Merchantable Form Factors 214 

178. Form Height 215 

179. Form Classes and Universal Volume Tables as Applied to Conditions in 
America 215 

CHAPTER XVII 

FRUSTUM FORM FACTORS FOR MERCHANTABLE 
CONTENTS IN BOARD FEET 

180. The Principle of the Frustum Form Factor 218 

181. Basis of Determining Dimensions of the Frustum 219 

182. Character and Utility of Frustum Form Factors 219 

183. Calculation of the True Frustum Form Factor 221 

184. Calculation of the Volume of Frustums. Influence of Fixed Versus Variable 

Top Diameters 221 

185. Construction of the Volume Table from Frustum Form Factors. A Short 

Cut Method 224 

186. Other Merchantable Form Factors for Board Feet 225 

CHAPTER XVIII 
THE MEASUREMENT OF STANDING TREES 

187. The Problem of Measuring Standing Timber for Volume 226 

188. The Measurement of Tree Diameters. Diameter Classes. Stand Tables . . 227 

189. Instruments for Measuring Diameters. CaUpers, Description and Method 

of Use 227 

190. The Diameter Tape 229 

191. The Biltmore Stick 230 

192. Ocular Estimation of Tree Dimensions 234 

193. The Measurement of Heights 235 

194. Methods Based on the Similarity of Isosceles Triangles 235 



TABLE OF CONTENTS xiii 

PAGE 

195. The Principle of the Klaussner Hypsometer 236 

196. Methods Based on the Similarity of Right Triangles 238 

197. Hypsometers Based on the Pendulum or Plumb-bob 239 

198. The Principle of the Christen Hypsometer 243 

199. The Technique of Measuring Heights 245 

200. The Measurement of Upper Diameters. Dendrometers 247 

201. The Biltmore Pachymeter 248 

202. The d'Aboville Method for Determining Form Quotients 248 

203. The Jonson Form Point Method of Determining Form Classes 249 

204. Rules of Thumb for Estimating the Contents of Standing Trees 251 

CHAPTER XIX 

PRINCIPLES UNDERLYING THE ESTIMATION OF 
STANDING TIMBER 

205. Factors Determining the Methods used in Timber Estimating 255 

206. Direct Ocular Estimate of Total Volume in Stand 256 

207. Actual Estimate or Measurement of the Dimensions of Every Tree of 

Merchantable Size 257 

208. Estimating a Part of the Timber as an Average of the Whole 257 

209. The Six Classes of Averages Employed in Timber Estimating 258 

210. The Choice of a System for Timber Estimating, with Relation to Accuracy 

of Results 261 

211. Relation betTween Size of Area Units and Per Cent of Area to be Estimated 262 

212. Degree of Uniformity of Stand as Affecting Methods Employed 265 

CHAPTER XX 
METHODS OF TIMBER ESTIMATING 

213. The Importance of Area Determination in Timber Estimating 267 

214. The Forest Survey as Distinguished from Timber Estimating 268 

215. Timber Appraisal as Distinguished from Forest Survey 269 

216. Forest Surveying as a Part of the Forest Survey 270 

217. The Cull Factor, or Deductions for Defects 271 

218. Total, or 100 Per Cent Estimates 271 

219. Estimates Covering a Part of the Total Area. The Strip Method 273 

220. Factors Determining the Width of Strips 274 

221. Method of Running Strip Surveys. Record of Timber 276 

222. Tying in the Strips. The Base Line 281 

223. Systems of Strip Estimating in Use 282 

224. Methods Dependent on the Use of Plots, Systematically Spaced 285 

CHAPTER XXI 

METHODS OF IMPROVING THE ACCURACY OF TIMBER 
ESTIMATES 

225. The Use of Forest Types in Estimating 288 

226. Method of Separating Areas of Different Types 290 

227. Site Classes and Average Heights of Timber 291 



xiv TABLE OF CONTENTS 

PAGE 

228. Methods of Estimating which UtiUze Types and Site Classes. Corrections 

for Area 292 

229. The Use of Correction Factors for Volume 293 

230. Methods Dependent on the Use of Plots Arbitrarily Located 297 

231. Estimating the Quality of Standing Timber 297 

232. Method of Mill Rmi Applied to the Stand 299 

233. Method of Graded Volume Tables AppUed to the Tree 299 

234. Method of Graded Log Rules Applied to the Log 299 

235. Combination Method Based on Sample Strips and Log Tally 300 

236. Limits of Accuracy in Timber Estimating 301 

237. The Co.st of Estimating Timber 302 

238. Methods of Training Required to Produce Efficient Timber Cruisers 303 

239. Check Estimating 308 

240. Superficial or Extensive Estimates 308 

241. Estimating by Means of Felled Sample Trees 310 

242. Method of Determining the Dimensions of a Tree Containing the Average 

Board-foot Volume 311 

243. The Measurement of Permanent Sample Plots 312 

Part III 
THE GROWTH OF TIMBER 

CHAPTER XXII 
PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

PAGE 

244. Purpose and Character of Growth Studies 315 

245. Relation between Current and Mean Annual Growth 316 

246. The Character of Growth Per Cent 318 

247. The Law of Diminishing Numbers as Affecting the Growth of Trees and 

Stands 318 

248. Yields, Definition and Purpose of Study 320 

249. Yield Tables 321 

250. The AppHcation of Yield Tables in Predicting Yields 322 

251. Prediction of Growth by Projecting the Past Growth of Trees into the 

Future 323 

252. The Effect of Losses versus Thinnings upon Yields 324 

253. The Factor of Age in Even-aged versus Many-aged Stands 325 

254. The Tree or Stem Analysis and the Limitations of its Use 326 

255. Relative Utility of Different Classes of Growth Data, and Chart of Growth 

Studies 327 

CHAPTER XXIII 
DETERMINING THE AGE OF STANDS 

256. Determining the Age of Trees from Annual Rings on the Stump 335 

257. Correction for Age of Seedling below Stump Height 336 

258. Annual Whorls of Branches as an Indication of Age 337 

259. Definition of Even-aged versus Many-aged Stands 337 



TABLE OF CONTENTS XV 

PAGE 

260. Average Age, Definition and Determination 337 

261. Determining the Volume and Diameter of Average Trees 338 

262. Determining the Age of Average Trees and of the Stand 339 

263. Age as Affected by Suppression. Economic Age 341 

CHAPTER XXIV 

GROWTH OF TREES IN DIAMETER 

Purposes of Studying Diameter Growth 342 

The Basis for Determining Diameter Growth of Trees 342 

The Measurement of Diameter Growth on Sections 342 

The Determination of Average Diameter Growth from the Original Data . 346 
Correction of Basis of Diameter Growth on Stump to Conform to Total 

Age of Tree 348 

Correlation of Stump Growth with D.B.H. of Tree 348 

Factors Influencing the Diameter Growth of Trees Growing in Stands .... 351 

Effect of Species on Diameter Growth 351 

Effect of Quality of Site 352 

Effect of Density of Stand .' 352 

Effect of Crown Class ; . 353 

Laws of Diameter Growth in Even-aged Stands, Based on Age 354 

Laws of Diameter Growth in Many-aged Stands, Based on Diameter 357 

Current Periodic Growth Based on Diameter Classes. The Increment 

Borer 358 

278. Method Based on Comparison of Growth for Diameter Classes 360 

279. Method Based on Projection of Growth by Diameter Classes 361 

280. Increased Growth, Method of Determination 363 

CHAPTER XXV 
GROWTH OF TREES IN HEIGHT 

281. Purpose of Study of Height Growth 365 

282. Influences Affecting Height Growth 365 

283. Relations of Height Growth and Diameter Growth 367 

284. Measurement of Height Growth 368 

285. The Substitution of Curves of Average Height Based on Diameter for 

Actual Measurement of Height Growth 371 

CHAPTER XXVI 
GROWTH OF TREES IN VOLUME 

286. Relation between Volume Growth, Form and Diameter Growth 374 

Tree Analysis, its Purpose and Application 374 

Substitution of Volume Tables for Tree Analyses 375 

Measurements Required for Tree Analyses 376 

Computation of Volume Growth for Single Trees 377 

Method of Substituting Average Growth in Form, or Tapers for Volume. . 379 

Substitution of Taper Tables for Tree Analyses 382 



xvi TABLE OF CONTENTS 

CHAPTER XXVII 
FACTORS AFFECTING THE GROWTH OF STANDS 

PAGE 

293. Enumeration of Factors Affecting Growth of Stands 384 

294. Site Factors or Quality of Site 384 

295. Volume Growth a Basis for Site Qualities 385 

296. Height Growth a Basis for Site Qualities 386 

297. Other Possible Bases for Site Qualities 387 

298. The Form of Stands, Even-aged versus Many-aged 388 

299. Annual Increment of Many-aged Stands 390 

300. The Effect of Treatment on Growth 391 

301. Density of Stocking as Affecting Growth and Yields 392 

302. Composition of Stands as to Species 393 

CHAPTER XXVIII 
NORMAL YIELD TABLES FOR EVEN-AGED STANDS 

303. Definition and Purpose of Yield Tables 395 

304. Standards for Yield Tables 395 

305. Construction of Yield Tables, Baur 's Method 396 

306. Standard for "Normal" Density of Stocking 397 

307. Age Classes 397 

308. Area of Plots 397 

309. Measurements Required on Each Plot 398 

310. Construction of Yield Table, with Site Classes Based on Height Growth. . 401 

311. Rejection of Abnormal Plots 404 

312. Construction of Yield Table, with Site Classes Based Directly on Yields 

per Acre 406 

313. Yield Tables for Stands Grown under Management , 407 

314. Yield Tables for Stands of Mixed Species 408 

CHAPTER XXIX 

THE USE OF YIELD TABLES IN THE PREDICTION OF 
GROWTH IN EVEN-AGED STANDS, WITH APPLICA- 
TION TO LARGE AGE GROUPS 

315. Factors Affecting the Probable Accuracy of Yield Predictions 412 

316. Methods of Determining Actual or Empirical Density of Stocking 413 

317. Application of Density Factor, in Prediction of Growth from Yield Tables 414 

318. Separation of the Factors of Volume, Age and Area 416 

319. Determination of Areas from Density Factor 416 

320. Application to Forest having a Group Form of Age Classes 418 

321. Determination of Volume and Area for Two Age Groups on Basis of Average 

Age 419 

322. Application of Results to Forest by Use of Stand Table and Per Cent. . . . 421 

323. Determination of Volume and Area for Age Groups on Basis of Diameter 

Groups 422 

324. The Construction of Yield Tables Based on Crown Space, for Many-aged 

Stands 422 

325. Apphcation of Method to Many-aged Stands 425 

326. Yield Tables for Stands Grown under Management 427 



TABLE OF CONTENTS xvii 

CHAPTER XXX 
THE DETERMINATION OF GROWTH PER CENT 

PAGE 

327. Definition of Growth Per Cent 429 

328 Pressler 's Formula for Volume Growth Per Cent 429 

329. Pressler 's Formula, Based on Relative Diameter 430 

330. Schneider 's Formula for Standing Trees 431 

331. Use of Growth Per Cent to Predict Growth of Stands 432 

332. Use of Growth Per Cent to Determine Growth of Stands by Comparison 

with Measured Plots 433 

333. Use of Growth Per Cent in Forests Composed of All Age Classes 434 

334. Growth Per Cent in Quality and Value 435 

CHAPTER XXXI 

METHODS OF MEASURING AND PREDICTING THE CUR- 
RENT OR PERIODIC GROWTH OF STANDS 

335. Use of Yield Tables, in Prediction of Current Growth 436 

336. Method of Prediction Based on Growth of Trees, with Corrections for 

Losses 436 

337. Increased Growth of Stands after Cutting 438 

338. Reduced Growth of Stands after Cutting 438 

339. Application of Yield Tables Based on Age, to Cut-over Areas 441 

340. Permanent Sample Plots for Measurement of Current Growth 443 

341. Measurement of Increment of Immature Stands as Part of the Total 

Increment of a Forest or Period . 443 

342. Comparative Value of Current Growth versus Yield Tables and Mean 

Annual Growth 445 

CHAPTER XXXII 

COORDINATION OF FOREST SURVEY WITH GROWTH 
DETERMINATION FOR THE FOREST 

343. Factors Determining Total Growth on a Large Area. 447 

344. Data Required from the Forest Survey 447 

345. Site Qualities, Separation in Field 448 

346. Relation between Volume and Age of Stands 449 

347. Averaging the Site Quality for the Entire Area 449 

348. Growth on Areas of Immature Timber 450 

349. Effect of Separation of Areas of Immature Timber on the Density Factor 

for Mature Stands 453 

350. Stand Table by Diameters for Poles and Saplings; When Required 454 

APPENDIX A 
LUMBER GRADES AND LOG GRADES 

351. Purpose of Log Grades 455 

352. Grades of Lumber , 455 

353. Basis of Lumber Grades 455 



xviii TABLE OF CONTENTS 

PAGE 

354. Grades for Remanufactured and Finished versus Rough Lumber 456 

355. General Factors which Serve to Distinguish Lumber Grades 456 

356. Grouping of Grades of Rough Lumber '. . . 457 

357. Example of Grading Rules 457 

358. Relation between Grades of Lumber and Cull in Log Scaling 458 

359. Log Grades, Determination 459 

360. Examples of Log Grades 460 

361. Mill-grade or Mill-scale Studies 461 

362. Method of Conducting Mill-scale Studies 462 

APPENDIX B 
THE MEASUREMENT OF PIECE PRODUCTS 

363. Basis of Measurement 466 

364. Round Products 466 

365. Poles 467 

366. Piling 470 

367. Posts, Large Posts, and Small Poles 471 

368. Mine Timbers 473 

369. Cross Ties 474 

370. Inspection and Measurement of Piece Products 477 

APPENDIX C 

TABLES USED IN FOREST MENSURATION (see Index of Tables) 479 

APPENDIX D 

BIBLIOGRAPHY 521 

INDEX 523 



44 


V 


48 


VI 


64 


VII 


66 


VIII 



TABLES 



Article No. Title page 

32 I Comparison of Results Obtained by Scaling the Cubic Con 

tents of Logs, at Small End and at Middle of Log 27 

38 II Comparison of Per Cents of Cubic Contents of Cylinders 
Scaled by Various Log Rules, for Logs 18 Inches in Diam- 
eter at Small End, with 2-inch Total Taper 37 

41 III Relation of Cubic and Board-foot Contents of 16-foot Logs 

with a Taper of 1 inch in 8 feet. Based on Tiemann's Log 
Rule ^-inch Saw Kerf 41 

42 IV Comparison of Blodgett and Tiemann Log Rules for Cer- 

tain Logs 42 

Effect of Different Methods of Scaling a Log 45 

Gain in Output Secured by Sawing around Compared with 

Slash Sawing in Per Cent of Latter Output 48 

Distribution of Waste between Slabbing and Sawdust 56 

Thickness of Plank to be Deducted for Slab Waste to Coin- 
cide with a Collar 1.5 Inches Thick. Sawdust Allowance 

20 Per Cent 61 

5^ IX Deductions for Slabbing and for Saw Kerf, for 12-inch Logs, 

in Ten Log Rules Based on Formulae 62 

Over-run, Doyle Rule, Texas 71 

Over-run, Doyle Rule, Ontario . 71 

Decimal Values below 12 Inches, for Scribner Log Rule 74 

Conversion of International Rule j-inch Saw Kerf for Other 

Widths of Kerf 81 

76 XIV Conversion of Log Rules with ^-inch Saw Kerf and No 

Shrinkage Allowance to Other Widths of Saw Kerf 82 

XV Per Cent of Increase in Sawed Lumber Caused by Sawing 

Lumber of Different Thicknesses 82 

XVI Correction in Per Cents for Contents of Logs in Superficial 
Board Feet, for Lumber Sawed Less than 1 Inch in Thick- 
ness 83 

Scaling Practice, or "Scale" in Different Logging Regions. . . 94 

Deductions for Crook or Sweep 116 

Solid Contents of Stacked Wood 127 

Standard Converting Factors for Cordwood 129 

Influence of Length of Stick upon the SoUd Cubic Contents 

of a Cord 130 

XXII Influence of Length of Stick on SoUd Cubic Contents of a 

Standard Cord, Balsam Fir 130 

XXIII Interdependence of the Stick Length and the Volume of 

SoUd Wood per Cord 131 

xix 



66 


X 




XI 


68 


XII 


76 


XIII 



83 


XVII 


93 


XVIII 


107 


XIX 




XX 


108 


XXI 



XX 



TABLES 



Article No. title page 

109 XXIV Solid Contents of a Standard Cord Based on Diameter of 

Stick. Average 4-foot Wood 131 

112 XXV Measurement of 4-foot Round Spruce Pulpwood, with Cull 

Factors Based on Solid Cubic Contents 134 

123 XXVI A Portion of a Volume Table Based on Mill Factors 147 

137 XXVII Preliminary Averages for Pitch Pine. Volume Table Based 

on Diameter and Total Height. 139 Trees. . 165 

139 XXVIII Comparison of Original and Harmonized Average Volumes. . 171 

140 XXIX Volumes Read from Curves of Volume on Diameter for 

Different Height Classes 171 

141 XXX Standard Volume Table Read from Curves of Volume on 

Height for Different Diameter Classes 174 

142 XXXI Local Volume Table, Form 175 

162 XXXII Conversion Factors for Second-growth Hardwoods by 

D.B.H. Classes with Corresponding Diameters of the 

Average 4-foot Stick in the Tree or in the Stack 181 

168 XXXIII Form or Taper for White Ash Trees of Different Diameters 
under 75 Years of Age, Giving Diameters Inside Bark at 

Different Heights above Ground 198 

XXXIV Tapers of Loblolly Pine, Two Trees 199 

183 XXXV True Frustum Ibrm Factors for Longleaf Pine, from Frus- 

tums whose Top Diameter Coincides Exactly with the 
Average Top Diameters of Trees of Each D.B.H. and 
Height Class 222 

184 XXXVI Frustum Form Factors for 555 Longleaf Pines, Coosa Co., 

Alabama. Based on Average Top Diameter of 13.2 Inches 

for Frustums 223 

XXXVII Actual Average Top Diameters of Merchantable Lengths, 
Longleaf Pine, Coosa Co., Ala. Basis 555 Trees. Average 

of all Top Diameters, 13.2 Inches 224 

Errors in Using Biltmore Stick 232 

Figures to be Used in Graduating a Biltmore Stick 233 

Table for Determination of Form Class of Trees by Means 

of Position of Form Point 250 

Relation of W^idth and Number of Strips to Area Covered . . 274 

Sizes of Circular Plots 286 

Relation between Plots and Area Covered 286 

Per Cent of Total Area Required in Estimating 292 

Comparative Estimates of a Tract of 40 Acres. Board Feet . 304 
Estimate of Taylor 's Creek Logging Unit, Blooming Grove 

Tract, Pike Co., Pa., 1911 309 

Growth of Jack Pine, Minnesota 318 

Yield Table for White Pine 321 

Yield Per Acre of Spruce, Cutting to Various Diameter 

Limits 322 

L Height of Seedhngs at Different Ages, Western Yellow 

Pine, Colfax Co., New Mexico 336 

LI Diameter Growth of Five Spruce Stumps 345 

LII Stump Tapers Based on Stump D.I.B. for Stumps 1 foot 

High 350 



191 XXXVIII 




XXXIX 


203 


XL 


220 


XLI 


224 


XLII 




XLIII 


228 


XLIV 


238 


XLV 


240 


XLVI 


246 


XLVII 


249 


XLVIII 


250 


XLIX 



257 

266 
269 



TABLES 



XXI 



UTICLE 


: No. 




LIII 


278 


LIV 


279 


LV 




LVI 


284 


LVII 


288 


LVIII 


290 


LIX 


296 


LX 


298 


LXI 


314 


LXII 




LXIII 


324 


LXIV 




LXV 



337 



339 



LXVI 



LXVII 



AppendLx. 


365 


LXVIII 




LXIX 


365 


LXX 




LXXI 




LXXII 




LXXIII 




LXXIV 


366 


LXXV 


370 


LXXVI 




LXXVII 




LXXVIII 




LXXIX 




LXXX 




LXXXI 



TITLE PAGE 

Growth of Loblolly Pine, Old Field, in D.B.H. Based on 

Age of Tree. Urania, La 350 

Current Growth of Spruce, Adirondacks Region, New York . 360 
Shortleaf Pine, Louisiana. Growth by Diameter Classes. . . . 362 

Current Growth, Loblolly Pine, by Diameters 363 

Height Growth of Chestnut Oak, Milford, Pike Co., Pa 371 

Growth of Chestnut Oak in Cubic Volume, from Diameter 

and Height Growth and Use of a Standard Volume Table 376 

Stem Analysis of a Tree 378 

Standards of Site Classification Based on the Height of Tree 

at 100 Years 387 

Average Crown Spread of Loblolly Pine in the Forest at 

Vredenburgh, Ala 389 

Normal Yield per Acre in Cubic Feet and Cords of Better 

Second-growth Hardwood Stands in Central New England 409 
Percentage of the Various Species in Mixture from Table 

LXII Classified as to T>-pe and Site Class 410 

Trees per Acre Based on Crown Space 425 

Yields of Cordwood, for Yellow Poplar in Tennessee — 

Based on Crown Space and Volumes of Trees of Given 

Ages 426 

Adirondack Spruce. Average Rate of Growth in Diameter 

on the Stump of 1593 Trees on Cut-over Land at Santa 

Clara, New York 440 

Areas Remaining Stocked on Cut-over Lands 443 

Relation between Circumference and Diameter for White 

Cedar Poles 467 

Minimum Dimensions of White Cedar Poles in Inches, 

Circumference, Classes 468 

Minimum Dimensions of Western Red Cedar Poles in Inches 470 
Minimum Dimensions of Southern Yellow Pine Poles in 

Inches, Circumference 471 

Minimum Circumference of Chestnut Poles in Inches 472 

Minimum Sweep Poles, Standard 472 

Minimum Sweep Poles, Country 473 

Dimensions for Pihng 473 

Board-foot Converting Factors for Various Products, U. S. 

Forest Service 478 

Cubic Contents of Cyhnders and Multiple Table of Basal 

Areas 480 

Areas of Circles or Table of Basal Areas for Diameters to 

Nearest ^Viiich 490 

Tables for the Conversion of the Metric to the English 

System, and Vice Versa 492 

The International Log Rule for Saws Cutting a J-inch 

Kerf 493 

Tables for Values in Schiffel's Formula for Cubic Volumes 

of Entire Stems 494 



XXll 



TABLES 



Article No. title page 

LXXXII Breast-high Form Factors 497 

LXXXIII Weights per Cord of Timber of Various Species, 7- to 8-inch 

Wood 498 

LXXXIV Tiemann Log Rule for Saws Cutting a ^-inch Kerf 500 

LXXXV Tiemann Log Rule Reduced to Small End Diameters 502 

LXXXVI Scribner Decimal C Log Rule 503 

LXXXVII Index to Standard Volume Tables 505 

LXXXVIII Index to Yield Tables 516 

LXXXIX Index to Taper Tables 519 



FOREST MENSURATION 



PART I 

THE MEASUREMENT OF FELLED TIMBER AND ITS 

PRODUCTS 



CHAPTER I 
INTRODUCTION TO FOREST MENSURATION 

1. Definition and Purpose. Forest Mensuration is that branch of 
forestry which deals with the determination of the volume of the wood 
material contained in logs or portions of felled trees, in standing trees, 
in stands of timber and in forests, expressed in terms of cubic measure, 
board measure, or any other unit. It also determines the growth and 
future yields of trees, stands, and forests in any of the above units of 
volume. The measurement of standing timber is termed Timber 
Estimating or Timber Cruising. The commercial measurement of the 
contents of logs is called Scaling. 

Forest property is land bearing forest trees as the principal vegeta- 
tion. The trees may be valued for their appearance, as in parks, their 
protective influences, as in forests at headwaters of streams, or their 
wood, as in all forms of commercial use, including by-products such 
as naval stores and bark. In past logging operations the land has not 
always been regarded as true forest property, capable of growing other 
crops of trees; but unless such land has a higher economic value for 
agriculture, grazing, or other purposes than for any of the three forest 
uses above mentioned, it is as truly forest property as the timber. 
The measurement of the volume and growth of timber is an indispen- 
sable factor in classifying lands for their highest use, whether for agri- 
culture or forestry. 

Forest Mensuration makes possible the systematic management 
of forest property by ordinary business methods, which require, first, 
a knowledge of quantities or amount of material, and its location and 



2 INTRODUCTION TO FOREST MENSURATION 

rate of production,^ and second, information on which to base the value 
of the property for the purpose of sale, exchange or the appraisal of 
damages. 

2. Relation between Lumbering and Timber Estimating. The 
logging of timber is usually conducted as a business venture entirely 
separate from the growing of trees or management of forest property, 
but whether this is so, or the forest owner cuts and logs his own tim- 
ber, the cost of the logging will depend in a great measure on the known 
quantity of timber which can be brought out over a given route and by 
a specific method of logging. The greater the volume of standing 
timber, the greater the investment which is justified in roads, railroads, 
chutes, or flumes to cut down the expense of hauling. Overestimates 
cause losses through excessive investments; underestimates cause losses 
through not investing enough money in these transportation systems. 
The logger cannot wait until his timber is cut and scaled before planning 
his operation. Accuracy in timber estimating is therefore an under- 
lying factor in the successful conduct of the business of lumbering. 

3. Relation between Forestry and Growth Measurements. Lum- 
bering as a business begins at the stump, while forest production may 
begin with the seedling, and may well be considered as a separate busi- 
ness enterprise. The growth of trees is the basis of returns on this 
business, no matter whether these returns are secured on the stump, or 
by means of the additional operation of logging. The speculator in 
standing timber hopes to realize a growth in unit prices such as was 
experienced as a result of the war. But the business of forestry depends 
for its profits on growth, first, in volume, and second, in quality, of the 
product by reason of increased sizes and improved texture, increase in 
prices being merely an additional guarantee of adequate returns. Since 
growth determines the quantity of products to be expected, any expen- 
diture in planting and care of the forest can be undertaken intelligently 
only when the probable rate of growth per acre is known. The study 
of growth is therefore a necessary part of the business of forestry and 
unless growth data can be obtained, there is no possible method of 

. 1 A business is an undertaking which seeks to supply a public demand. The 
most common form of business is that which produces raw materials and transforms 
them into finished products delivered as such to the consumer. Any distinct step 
in this process may and often does constitute a separate business. To accomplish 
the purpose of its existence, a business deals with three factors, quantity, location, 
and time. To supply forest products for the innumerable demands of modern 
civilization, a well-conducted business operation requires full knowledge of the 
quantity of raw material and finished products with which it deals, their location, 
and the time or periods when these quantities wall be available. Forest Mensura- 
tion is as fundamental to forest production as is inventory and merchandise account 
to a mercantile business. 



RELATION OF MENSURATION TO FORESTRY SUBJECTS 3 

determining either the proper investments and expenses, or the probable 
returns and profits from such an enterprise. 

4. Relation between Forest Mensuration, Stumpage Values and the 
Valuation of Forest Property. In determining the value of forest 
property for sale, exchange, or the appraisal of damages, it is necessary 
first to know what the mature standing timber is worth on the stump 
previous to cutting. This is known as stumpage value. The stumpage 
value of standing timber is derived from the value of the finished prod- 
ucts and is influenced by four factors, namely, the species of wood, 
its quantity, its quality, and the unit price of the product. Forest 
mensuration by means of a forest survey determines as accurately as 
possible the first three factors. By determining through an appraisal 
the price of stumpage for the different kinds and qualities of timber 
found on the area, the value of the timber may be found. 

The value of young timber and of forest soil can be calculated after 
the possible yields at given ages have first been approximated and the 
stumpage value has been appraised for this final yield. 

5. Relation of Mensuration to Other Forestry Subjects. The rela- 
tion of Forest Mensuration to other subjects in forestiy is shown in 
Fig. 1. In the threefold division of forestry indicated, mensuration 
falls in the mathematical or business group, but is included in the phys- 
ical branch of that group which deals directly with the forest. 

Mathematics is the basis of Mensuration, since the latter subject 
deals primarily with quantities. But as both timber estimating and 
growth data must usually be expressed on terms of area or acreage. 
Mensuration rests directly on Surveying. 

Mensuration in turn furnishes the quantitative data required by 
the science of Forest Finance as a basis on which to compute the cost of 
production and the probable returns from forestry and to indicate the 
choice of methods to use in forest production. Although it falls in the 
business group, and is a basic subject underlying Forest Management, 
Mensuration is a statistical science similar to Forest Finance. Neither 
subject constitutes an applied science, which is the characteristic of 
Forest Management. Mensuration is therefore not a direct subdivision 
of Management, but a distinct subject preparatory to Management. 

6. Absolute versus Relative Accuracy in Mensuration. Forest 
Mensuration attempts to secure as close an approach to mathematical 
accuracy as the conditions of the problem, the use to which the data are 
put, and the cost of the work will permit. In scaling, the volumes of 
logs are determined before sawing, and in timber estimating, the contents 
of trees and stands are obtained before felling. But no log rule will 
give the exact quantity of lumber which will be sawed from a given 
log, and no tree volume table can predict the output in boards from a 



4 INTRODUCTION TO FOREST MENSURATION 

given tree, since these results will vary with the methods and conditions 
of sawing and of utilization. 



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Dendrology 
Forest Ecology 
Forest Entomology 
Wood Technology 




Silviculture 
Forest Engineering 
Lumbering 

Wood Using Industries 
Forest Protection 


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Botany 
Zoology 
Mechanics 




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Again, in estimating timber it is seldom possible to measure every 
tree, on account of the time and expense involved. For this reason, 



FOREST SURVEY 5 

only an average portion of the stand may be measured. The laws of 
averages, or of sampling are applied to solve nearly every problem in 
Forest Mensuration, in order to bring the cost of the field work within 
practical limits. 

When Mensuration deals with the growth of trees and stands, and 
of whole forests, its purpose is to predict what will occur in the future. 
It bases these predictions upon the results which have occurred in the 
past, under conditions judged to he similar to those which will affect 
these future stands. The laws of growth of trees, and especially, of 
stands composed of great numbers of trees competing with each other 
for existence and supremacy, can only be approximated on the basis of 
probabilities and averages. The results of living forces cannot be 
predicted with mathematical accuracy, and the study of growth par- 
takes of the nature of research rather than of routine measurement of 
definitely determinable quantities. 

Neither Forest Mensuration nor Forest Surveying produces any 
physical change or improvement in the forest, as does the application of 
silviculture, protection, and lumbering. The achievements of forestry 
depend upon the amount and character of the actual work done along 
these latter lines. Misdirected work, done at the wrong time or place 
and in the wrong quantity, or by too expensive a method when com- 
pared with results, means waste, inefficiency, and ultimate ruin and 
bankruptcy of the enterprise. The data supplied by mensuration and 
supplemented by forest finance are the balance wheel of forest industry. 
But the necessity of restricting the funds expended upon the mere col- 
lection of data to as small a per cent as possible of the total budget of 
expenditures, reserving the greater portion for the operations which 
effect actual change in the forest, is obvious and justifies the use of meth- 
ods based on averages rather than extreme mathematical accuracy. 

7. Forest Survey. Forest Survey is the general term applied 
to the project of gathering all the quantitative data required regarding 
a specific forest property. It includes a survey and maps of the area, 
thus locating the property and its subdivisions, a measurement of the 
volume and character of the timber, and it may cover other resources 
such as land classification, waters, forage, game, and fish. Forest 
Surveying and Forest Mensuration deal with the principles and methods 
of accomplishing this work. The Survey itself is the enterprise or 
project of securing the data. Accuracy in the results of a forest survey 
is judged, not on an absolute standard, but in relation to the balance 
between utility of the results and the cost of obtaining them, and is 
therefore always a relative term. 



CHAPTER II 
SYSTEMS AND UNITS OF MEASUREMENT 

8. Systems of Measurement Used in Forest Mensuration. 

Throughout the United States and Canada the EngUsh system of 
measure is used in all practical applications of Mensuration. In the 
Philippines the metric system is the standard. (Appendix C, Table 
LXXIX.) Efforts to substitute the metric sj^stem in the United States 
for the units established by custom have so far failed, though its use 
was sanctioned by Congress in 1866. Mensuration is applied more 
generally to the solution of practical problems such as timber estimating 
than to purely scientific research, and for the former, the results must 
be expressed in the customary units to be intelligible. Scientific forest 
measurements have also, except in a few instances, been expressed in 
English units. 

In measuring distances and areas, the chain of 66 feet, or 4 rods, 
is a commonly used unit. Five chains constitute a tally, or 20 rods; 
and 16 tallies, or 80 chains, equal 1 mile. One tally forms the side of a 
square 2^ acres in area. Distances are commonly measured by pacing, 
or counting the number of paces, the average length of the individual 
pace having been determined by previous tests. A true pace is the 
swing of one foot, or twice the length of a step. In counting, the pace 
rather than the step should be used, since it reduces the count by half. 

The acre, containing 160 square rods or 43,560 square feet, is the 
unit of area. In the rectangular system of survey adopted by the 
United States the following definitions apply: 

Township — a tract approximately 6 miles square containing 
36 sections. 

Section — a rectangular tract containing approximately 1 square 
mile or 640 acres, but which may contain more or less 
than this area in irregular surveys. 

Quarter Section — a subdivision of a section containing approxi- 
mately 160 acres. 

" Forty " — a colloquial term describing a ygth section or quarter 
of a quarter section containing approximately 40 acres. 

Lot — a tract ordinarily containing not less than 20 or more than 
60 acres, but which may contain less area, of either 
6 



PIECE MEASURE 7 

rectangular or irregular shape, and which takes the place 
of the " forty " in irregular surveys or bordering lakes 
or streams.^ 

In measuring trees, the foot is the standard for height, and the 
inch, divided into tenths of inches, for diameter. Basal area is the cross- 
sectional area of a tree or stand, in square feet, measured at 4| feet from 
the ground. This is obtained from area of circles whose diameters equal 
those of the trees measured. 

9. Piece Measure. Wood products which are used in the round, and 
logs or bolts which are barked, shaped, and reduced to standard dimen- 
sions where felled, are usually measured and sold by the piece. These 
pieces are graded by size and by quality into accepted pieces and culls, 
or rejects, whose defects render them unfit for the special purpose 
required. The standard sizes are determined by specifications, which 
also prescribe the species of tree and the required quality of the product. 
The principal products purchased on this basis are cross ties, poles, 
posts, piles, and mine timbers. 

Where bolts of uniform size are sawed or split for manufacture 
into special products, they may be counted and paid for by the piece. 
Their average volume is determined beforehand. When the number 
of pieces per cord, or per thousand board feet is agreed on, the payment 
may be in terms of these latter units. 

Linear measure is sometimes used for pieces of standard width and 
thickness but of variable length. Such products are sold by the lineai* 
foot. This standard is widely used for piling. 

10. Cord Measure. When the pieces into which trees are sawed or 
split are of lengths shorter than ordinary logs, and of irregular shape, 
the expense of determining separately the contents of each piece is 
avoided by stacking them in regular piles or cording them up, and 
measuring only the exterior dimensions of the stack to get the total 
stacked cubic space occupied. This stacked cubic measure does not 
indicate the solid contents, which may vary widely. But if the average 
per cent of solid contents per cubic foot of stacked measure is known for 
sticks of given sizes and character, this stacked measurement becomes 
a practical and serviceable standard, though not well suited to scientific 
investigations. 

The cord is the standard generally adopted for stacked wood. 

1 References. Manual of Surveying Instruction for the Survey of the Public 
Lands of the United States and Private Land Claims, Commissioner of the General 
Land Office, Washington, D. C, Government Printing Office, 1902. 

Manual for Northern Woodsmen, Austin Cary, Part I. Section VIII, 1918. 
Harvard University Press, Cambridge, Mass. 



8 SYSTEMS AND UNITS OF MEASUREMENT 

The standard cord is 4 by 4 by 8 feet, containing 128 cubic feet. There 
are, however, other cord units in use (Chapter IX). 

11. Cubic Measure. The cubic volume of trees and logs affords 
the only basis of accurate and permanent scientific records, and a uni- 
form standard of measurement. For this purpose the cubic foot should 
be used as the standard unit. 

Where cubic volume was employed by lumbermen, other cubic 
units, whose contents were based on cylinders of given sizes, have been 
adopted arbitrarily. These units possess no advantages over the cubic 
foot (Chapter IV). 

In most regions, the desire to express the contents of logs in terms of 
sawed lumber prevented the adoption of the cubic foot as the standard 
of measurement for logs. 

12. Board Measure. Board measure may be defined as a cubic 
standard for measuring sawed lumber. A board foot is a board 1 foot 
square and 1 inch thick. Twelve board feet of sawed lumber equal 1 
cubic foot. The board-foot contents of sawed lumber is found by 
multiplying the product of the width and thickness in inches by the 
length in feet and dividing by 12. 

13. Log rules. A log rule is a table giving the contents of logs of 
different diameters and lengths. The unit of volume used may be 
based on cubic measure, or board feet. The latter form of table differs 
from that based on cubic contents since it indicates only the net volume 
of the product in boards which result from sawing the log. The use of 
such log rules is to measure the contents in the log before sawing, as 
a basis of sale of logs or for other purposes requiring such measurement. 
Fixed or arbitrary values are assigned or agreed upon for logs of each 
diameter and length. The table thus becomes a standard of measure- 
ment based upon a unit of volume. 

This method of measuring logs has consequently led to the develop- 
ment of numerous log rules whose construction is discussed in Chapters 
IV, V and VI. These rules differ, some of them greatly, for logs of 
the same dimensions. 

To secure the universal adoption of a single log rule which is at once 
accurate and acceptable is probably an impossible task, and several of 
the more widely used ones will no doubt continue as standards. 

14. Measurement of Standing Timber, Postponed till after Manu- 
facture. This lack of standardization as to units for board-foot contents 
of logs inevitably reacts upon the accuracy and consistency of measure- 
ments of the board-foot contents of standing timber. The contents 
of a given stand will vary widely with the log rule used in estimating. 

The custom of estimating standing timber in terms of the product 
is not confined to measurement by board-foot log rules. Hewn ties, 



MEASUREMENT OF STANDING TIMBER IN THE TREE 9 

poles, staves and other piece products are customarily used as units for 
timber estimating, when the timber is to be used for these purposes. 

Thus the standard commonly sought in America for measuring stand- 
ing timber is the net merchantable volume, which results from deducting 
all forms of waste in manufacture from the total contents of the tree. 

There is but one accurate method of measuring this net contents, 
and that is to postpone the measurement until the timber is logged 
and manufactured into boards or other products. Since a purchaser of 
standing timber is always conservative wherever a doubt exists, it is to 
the owner's interest to sell on the basis of actual mill cut of boards or 
output of other products, whenever this is possible. This basis is 
often used in regions where the timber is cut by small portable mills, 
located in or near the tract and where small amounts are purchased. 

15. Measurement of Standing Timber Postponed till after Logging. 
Where the logs must be driven down streams or hauled long distances 
by the purchaser, this basis becomes impractical both because of the 
delay in settlement of account and the difficulty of checking the output 
of lumber. The timber owner is thus forced to substitute a log scale for 
a mill tally of lumber. This scale is always based on some log rule agreed 
upon beforehand, and may or may not give results coinciding with the 
actual sawed output. If the log rule is known to be inaccurate, the 
excess or deficiency of manufactured products can be ascertained only 
by a comparison of the mill tally with the log scale. Such comparisons 
will give an idea of over-run or under-run (§46). The owner can then 
adjust the price in. subsequent sales of logs according to the difference 
between the scaled contents of his logs and their probable output in 
sawed lumber. 

16. Measurement of Standing Timber in the Tree. But even the 
log scale is inapplicable when standing timber is purchased in large 
amounts and a long period is required for completion of logging. The 
owner desires prompt payment even if based on a less accurate measure- 
ment of volume. The volume of the standing timber must be measured 
as well as possible, and since, at best, onl}^ the diameter of the trees 
together with a few heights can be actually determined and the rest of 
the work is done ocularly or by guess, the result is only a rough estimate. 
This method has given rise to the term Timber Estimating. The prin- 
cipal sources of error in timber estimating lie in the effort to arrive at the 
net merchantable contents minus waste, in the use of inaccurate and 
variable standards of log measure for this purpose, and in the difficulty 
and cost of determining even the superficial dimensions of standing trees. 
This leads to short-cut methods, approximations and guess work and 
calls for the development of system and of personal skill. One improve- 
ment in timber estimating widely used by foresters is the tree-volume 



10 SYSTEMS AND UNITS OF MEASUREMENT 

table, which gives the average contents of entire trees of different dimen- 
sions, in terms of standard log rules or other units, thus eliminating a 
certain amount of ocular work. 

17. Need of Standardization for Both Commercial and Scientific 
Measurements. The justification of the use of standards which give 
the contents of standing timber in terms of products, rather than 
actual cubic volume, lies in the fact that the value of the timber, standing 
or cut, depends upon the volume and quality of these products and not 
upon the cubic volume. 

Had it been possible to secure the adoption of a uniform standard 
of conversion into board feet, the use of this standard would be more 
serviceable than the apparently simpler cubic standard. But in prac- 
tice the same motives which here gave rise to standards based on products 
have led the French to adopt, as substitutes for cubic measurement, 
rules of thumb which are less accurate by far than many of our log 
rules. ^ 

The greatest drawback to the use of units intended to measure 
the product directly lies not in their character but in their inaccuracy 
and in the multiplicity of standards. It is easily seen that volume 
tables and measurements of growth which are based on some widely 
used commercial log rule may coincide with custom, but are incapable 
of use or comparison with other log rules (§ 77) and are inaccurate as 
a scientific basis of measuring growth or volume. This fact has led to 
endless duplication of effort and has been the chief reason for the lack 
of real progress in accumulating standard data on volume and growth 
of American trees. 

A continuance of such duplication of effort will hinder the progress 
of forestry in America, which must depend in a large part upon the 
accuracy of volume and growth data gathered by forest measurements. 
While the local value of data based on log rules sanctioned by custom 
will continue, these field data should be gathered in such form as to be 
of permanent value independent of these variable local standards. 

It is possible to convert all measurements to the common standard 
of cubic feet, which gives a basis of scientific comparison between the 
volumes of different trees and species, and a permanent basis for measure- 
ment of growth for trees and stands. It is also possible to adopt, for 
the purposes of permanent record, a log rule based on scientific principles 
which will give an equally reliable comparison of the contents of trees in 
board feet and the growth of stands expressed in this unit of product. 

But for a permanent record from which the volumes of trees may be 
derived in any unit of product, standard or local, the average form of the 

1 Mensuration in France, Donald Bruce, Journal of Forectry, Vol. XVII, 1919, 
p. 686. 



FORMS OF PRODUCTS 11 

tree is required, as expressed in diameters at different points on the 
stem. Investigations of tree form are therefore at the root of all per- 
manent progress in Mensuration (Chapter XVI). 

18. Forms of Products into which the Contents of Trees are Converted. The 
products manufactured from trees may be classed according to the following group- 
ing: 

Group I. Manufactured products of definite form, retaining the wood structure 
and requiring waste in manufacture. 

A. Manufactured from logs. 

1. Lumber 

a. For construction. 

1'. Structural timbers. 

2'. Dimension. 

3'. Boards. 

4'. Remanufactured or planing mill products. 

5'. Special products. 

6'. For export. 

b. For remanufacture. Scjuare edge or round edge. 
1.' For mill work, furniture, fixtures. 

2.' For utensils and supplies. 
3.' Boxes and containers. 

2. Veneers. 

3. Manufactured direct from log for finished articles. 

B. Manufactured from bolts. 

Billets, flitches, squares, blocks, shingles, spokes, staves, etc. 

C. Manufactured from mill refuse, i.e., from slabs, trimmings and 

edgings. Shingles, lath, bo.xboards, etc. 
Group II. Bulk products in which the form or both form and structure are 
destroyed. 

1. Excelsior. 

2. Wood pulp. 

a. Mechanical. 

b. Chemical. 

3. Distillates. 

4. Extracts. 

5. Fuel. 

a. Charcoal, 

b. Fuel wood. 

6. Bark. 

Group III. Piece products retaining in whole or in part the original form. 

1. Round products, 
Poles, piling, posts, etc. 

2. Shaped products. 
Hewn cross ties. 

1'. Standard ties. 
2'. Mine ties. 

Group I. In converting round logs into lumber, there is unavoidable waste in 
sawing due to the difference in shape between the products desired and the log, 
and to the saw kerf. The per cent of waste depends upon the dimensions of the 



12 



SYSTEMS AND UNITS OF MEASUREMENT 



smallest board which is merchantable, and upon the thickness of saw used. Further 
intensive utilization of slabs (pieces slabbed off from the round surface of logs in 
sawing) and of edgings (pieces cut from the edges of boards to give parallel edges 
and remove bark), by manufacture into sawed products depends upon finding a 
market for pieces whose size is small enough to permit of their manufacture from 
these otherwise waste products. 

The waste in manufacturing articles direct from the log depends on the shape 
of the manufactured article with reference to the bolts from which it is made. Unless 
profitable use can be found for the portions so wasted, or unless antiquated methods 
and machinery are in use, the portions of a tree or log lost in manufacture cannot 
be regarded as wasted, any more than the loss in bulk of a rough block of stone in 
process of transformation under a sculptor's hand is considered waste. It is for 
this group that log rules are required. 



"Woods Wast 

16.6i« 

. ^ s 


e 


Mill Waste 
44.3^ 








Lumber 
89.1;* 




Z' 








A 


Tops 

Limbs 

Stumps 






O P 

■^*- a- 


Edgings 
Trimmings 




-^ re 

» » 

ft) 3 


Seasoned 

L^nplaned 

Lumber 

33.5J« 



•'Careless mfg. 
miscellaneous 2.556 

5 TYPICAL INDUSTRIES 
Rough Lumber 100^ 



"1 2 ^ 
(D o 5^ 



Factory Waste 



Finished Product 



Planing Mill Products 



96!« 



m 



Car Construction 



Boxes 



82^ 



255« 



75^ 



Vehicles 



755^ 



" ^ ea 



c 5 «! 



Fig. 2. — The percentage of utilization of the volume of a tree when manufactured 

into lumber. 



Group II. To this group belong also those waste products from Group I for 
which use as bulk materials can be found. The characteristics of this group are 
that the entire volume of the log, and a much larger per cent of the volume of the 
tree is utilized than in Group I. Material may be taken to very small diameters, 
since size is not a requisite of utility but merely a convenience in handling. For 
this group, cubic volume is the required standard of measurement, and the use of 
stacked cubic measure is customary. 

Group III. Nearly all the round or shaped products in this group may also be 
obtained from larger logs by sawing as poles, ties, fence posts, in which case they 
can be measured for their contents in sawed lumber. For round i)roducts, as poles, 
piles or posts, or for hewn products, as hewn or " pole " ties, the number of pieces 
of standard sizes and shapes is the simplest method of measurement. For this 
group the important factor in measurement is the set of specifications which deter- 
mine the grades of product. The waste to be expected in manufacture under Group I 
is shown in Fig. 2. 



THE FACTOR OF WASTE IN MANUFACTURE 13 

19. The Factor of Waste in Manufacture. A waste product is one for which a 
profitable use has not been found. It is not sufficient that the product could be used 
for some purpose if it could be transported to some place other than the site of its 
first appearance as waste. The value of the product must be such as to bear the 
cost of manufacture and transportation plus a profit. Unless some portion of a 
tree yields products which fulfill these conditions, the whole tree remains unutilized 
to finally die and rot, a true waste product of nature. In inaccessible places, entire 
stands go to waste. 

Waste in tops and limbs represents those portions of the tree which under the 
existing conditions do not yield profitable products. But little deliberate or inexcus- 
able waste occurs over any long period without discovery and correction. The 
per cent of waste for unprofitable portions of the trees is often as high as 50 per cent 
for staves or other special products and 25 per cent or over for lumljer. The average 
of 16.6 per cent shown in Fig. 2 for lumber is far too high for bulk products such 
as pull) wood or for trees with small limbs and boles of regular form. 

Bark is a typical example of a "waste" product. As fuel, it is not wasted. When 
tannin extract or cork is yielded it is carefully gathered. For lumber, it is entirely 
wasted, except as incidental fuel. The waste in sawdust, slabs, edgings and factory 
finishing, when reduced to the lowest possible terms by good machinery, can hardly 
be regarded as avoidable waste, since the product which results from this apparent 
waste has a value much higher and a utility much greater than before the " loss " 
of the extra bulk. 

When this sawdust and refuse is used as fuel in the mill, as is now the common 
practice, it replaces coal, thus not only effecting a great economy but performing an 
important public function in saving transportation costs on coal. The only real 
waste in manufacture is where methods are used which unduly increase sawdust 
and slab waste at the expense of finished products. Waste caused by seasoning of 
wood is not avoidable, and increases the value of the product in greater ratio than 
its loss in bulk. 

The per cent of actual avoidable waste in utilization of the tree is difficult to 
determine or to prove. It constitutes the per cent of difference between what is 
utilized in higher forms, and what could be utilized under the same economic condi- 
tions, at a profit. It is a measure of the efficiency and alertness of the operator, 
and will seldom exceed from 5 to 10 per cent even under exceptionally bad conditions; 
while under good management this avoidable waste is probably not over from 2 to 
5 per cent. 

The utilization of small-sized pieces and bulk products not only reduces the per 
cent of waste in single trees, but brings entire trees of smaller dimensions into the 
merchantable class, thus increasing the per cent of volume in a stand of timber 
which is merchantable, and lowering the age at which trees can be marketed. Since 
the number of trees per acre rapidly diminishes with increasing size, close utilization 
of small diameters will very greatly increase the per cent of merchantable volume 
in young stands and reduce the per cent of waste by natural losses of trees before 
they reach the larger diameters. 

20. Actual versus Superficial Contents of Sawed Lumber. The variation 
between actual cubic contents of sawed lumber, and the superficial contents as 
expressed in board measure, must not be overlooked in Forest Mensuration. Log- 
rules for board feet are uniformly based on the sawing of boards 1 inch thick. Mill 
tallies of lumber which is sawed scant, such as |-inch boxboard material, will con- 
sequently greatly overrun the scale of the logs, in so-called superficial feet, which 
is the number of square feet of surface measure regardless of thickness. On the 



14 SYSTEMS AND UNITS OF MEASUREMENT 

other hand, hardwoods are customarily sawed to thicknesses sHghtly greater than 
1 inch to allow surfacing down to full inch thickness, and this practice reduces the 
superficial yield in board feet as compared to softwood species which are commonly 
sawed scant. Either practice causes the actual output measured in board feet 
(§ 12) to differ from the scaled contents of the logs. The actual dimensions of board 
which are accepted as inch lumber and. other standard thicknesses, and the amount 
of difference, scanting or extra thickness, permitted, is standardized by trade prac- 
tice for each region and species.^ 

These differences in sawing affect the over-run of sawed lumber, which for the 
same log rule would thus be greater for softwoods than for hardwoods. 

21. Round-edged Lumber. Most lumber is square edged in sawing. Close 
utilization by the box, match, sash and blind, woodenware, furniture and certain 
other industries has led to the sawing of logs " alive " or through and through into 
boards from which the waney edges are not removed by squaring. These boards, 
except when sawed from the middle of the log, have one face narrower than the other 
and owing to the taper of the log, the faces are not of uniform width throughout 
their length. As the lumber in such boards is closely utilized, its board-foot contents 
is computed by measuring the average wddth of the narrow face. The thickness 
is considered on the same basis as for square-edged lumber. Lumber of this char- 
acter is usually cut by portable sawmills and sold direct to factories. The scale 
at the factory is used to check that at the mill. This prevents taking advantage 
of the uncertainties of the method. The logging and sawing are paid for on the 
basis of the mill scale, which scale usually becomes the standard for measuring the 
contents of the standing timber. 

Round-edged lumber will yield from 10 to 20 per cent more scale than square- 
edged, the excess being greater, the smaller the logs sawed. For plank 2 inches 
or more in thickness, a loss is incurred both in utilization and in scaling by reason 
of the wane, which causes an excessive difference in width of the two faces. This 
loss is reduced by cutting 1-inch boards from the sides of the log (§ 51). 

Closeness of utilization of the tree and stand is increased by this method of saw- 
ing. Tops are sometimes taken down to 2 inches and never to greater than 4 inches. 
Branches which crook only in one plane are used. 

22. Products Made from Bolts and Billets. Bolts are sections of logs still in 
the round, and less than 8 feet long, i.e., too short to be conveniently measured as 
logs. Billets are obtained by halving, quartering, or otherwise splitting or sawing 
bolts lengthwise. Bolts may be split into billets, each of which is intended to pro- 
duce one finished article, such as a wagon spoke or stave. These are measured by 
count. Billets of larger size may also be split from bolts. So-called shingle bolts 
are billets split or sawed from large trees, or blocks from thick slabs. 

Billets are also obtained by sawing bolts, and are then termed flitches, squares, 
slats, or blocks. Squares are used in turning out round articles, such as shuttles, 
spools and bobbins. On account of their regular form, squares are sold by count, 
or by bulk, on standards agreed on, the price being based on either the number or 
the board-foot contents. They may be sold by stacked cords. Bolts, and split 
or sawed billets of irregular form, not yet manufactured into squares, are sold by 
stacked cubic measure except in the case of bolts over 12 inches in diameter and over 
4 feet long, which may be scaled by a log rule. The width of the stack is determined 
by the length of the product and may range from 22 inches to 5 feet and over. In 

1 Lumber and its Uses, by R. S. Kellogg, 1914, Radford Architectural Company, 
Chicago, Illinois. 



PRODUCTS MADE FROM BOLTS AND BILLETS L5 

this case a cord is a stack 4 by 8 feet but whose width is that of the given product 
(§ 99). 

Different customs prevail in different industries. Shingle bolts (split or sawed 
billets) are sold in lengths which allow three cuts. For 16-inch shingles, with 4 
inches for trimming, the piece is 52 inches long. For 18-inch shingles, a length of 
58 inches is required. The cord is 4 by 8 feet by the indicated width. 

Spoke manufacturers dealing in standard 30-inch spoke_ billets compute a 
cord as 4 by 8 by 2| feet, or 80 cubic feet. Others measure the cubic contents, 
using 128 feet for a cord. In the stave industry a cord measuring 4 by 11 feet by 
the length of the stave bolts is quite common. For 36-inch billets this gives 132 
cubic stacked feet, but the rule is applied to billets of other lengths. 

Billets and bolts for tool handles are always measured by the rank, in cords 
measuring 4 by 8 feet by the required width. 

References 

Measuring and Marketing Woodlot Products, Wilbur R. Mattoon and William B. 

Barrows, Farmers Bulletin, 715, U. S. Forest Service, 1916, 
Wood Using Industries of New York, John G. Harris, U. S. Forest Service, New 

York State College of Forestry, Series XIV, No. 2, 1917. 



CHAPTER III 
THE MEASUREMENT OF LOGS. CUBIC CONTENTS 

23. Total versus Merchantable Contents. Logs are measured to 
determine their total cubic contents with or without bark, or they 
are scaled for merchantable contents only. The total cubic con- 
tents is required in scientific studies of volume and growth and for 
such commercial purposes as make use of the entire volmiie of the log. 
The cubic contents is found by measuring the length and the diameter 
at one or more cross sections and computing the volume of the log as a 
whole, or by sections, from these measurements. Where the thickness 
of bark is measm-ed, the difference in volume of the log measured out- 
side and inside the bark gives the volume of bark. 

24. Log Lengths. Softwood or coniferous logs are usually cut into 
even lengths, or multiples of 2 feet, and may be any length from 8 feet 
to over 60 feet, being limited only by the height and upper merchant- 
able diameter of the tree, the length of material demanded for manu- 
facture, or the convenience of transporting long versus short logs. 
Logs, especiallj' hardwoods, are sometimes cut to odd lengths or multi- 
ples of 1 foot. The standard commercial lengths for softwood logs 
vary from 10 to 22 feet, and average 16 feet. In hardwoods, log lengths 
average somewhat shorter, since utilization of shorter lengths is more 
common. Log lengths are marked off on the felled tree by notching 
with an axe. It is customary to use a wooden measuring stick 8 feet 
long, and divided into 2-foot lengths.^ 

For exact measurement of length, the steel tape, graduated to feet, 
and tenths instead of inches, is used. The log length is measured along 
the surface, which is assumed to equal the length of the axis. For 
commercial uses, an excess length of from 2 to 6 inches is required as a 
margin for trimming. For total cubic contents the logs or sections are 
measured to their actual lengths. 

' The accidental chopping off of the top of the measuring stick sometimes results 
in short measurements. In some regions, notably in Southern pine, careless measure- 
ment of log lengths resulting in excess trimming allowance and odd lengths causes a 
waste in woods and mill, in trimming to standard sizes, of from 3 to 5 per cent of the 
total cut. This statement is based on careful measurements covering 14 years' 
experience in six states with eight different companies. 

16 



DIAMETERS AND AREAS OF CROSS SECTIONS 17 

25. Diameters and Areas of Cross sections. Cross sectional areas 
are assumed to be circular in form, and were this assumption correct 
the measurement of any. average diameter would give the cross section. 

If B =" basal" area, or area of circle, 

D = Diameter of circle, 

7r= Ratio, or 3.1416. 
Then 

2?=-— = .7854D2. 
4 

But practically every cross section departs slightly from a true 
circle, and a large proportion are very eccentric, some showing a dif- 
ference of several inches between their longest and shortest diameters, 
and having an elHptical or oval form.^ 

No attempt is ever made to compute the actual cross sectional area 
of such eccentric sections. Instead, two diameter measurements are 
taken at right angles and the average of these is assumed to be the 
average diameter. A circle with corresponding diameter is assumed to 
have the same cross sectional area as that of the actual section. Usually 
the longest diameter is taken, and one at right angles to it, through the 
geometric center of the section.^ 

Abnormal cross sections are occasionally encountered in which the average 
diameter of the section and its area are either too large or too small to give the volume 
accurately owing to some distortion in form of the log as a whole or of the portion 

1 The area of an ellipse is 

TrDd 
B = -, 

4 

when D and d represent the long and short axes. 

D+d 

The area of a circle whose diameter is calculated as ■ is 

2 

n = . 

4(2) 

Then 

w(D+dy- irlM _Tr (D-dy 

4(2) 4~"4 (2) ' 

which is equal to the area of a circle whose diameter equals one-half the difference 
between D and d. This correction which is always minus, is ignored in measuring 
cross-sections. 

2 In determining the average diameter, no attention is paid to the growth rings 
or the position of the pith or growth center of the section. In eccentric cross sections 
the pith is always found some distance to one side of the geometric center, which is 
the point through which the diameter measurement must fall. 



18 THE MEASUREMENT OF LOGS. CUBIC CONTENTS 

measured. Abnormally large sections are found at forks or at the base of limbs or 
are caused by swellings. Stumps cut low give a section averaging much too large 
to indicate the true volume of the log, due to the rapid flare of the butt. 

Abnormally large diameters at the top end of logs should be measured by reduc- 
ing the diameter to what the log would have if it held its regular form. Where 
flaring butts are measured, the errors incurred may be serious. It is preferable to 
adopt a method which does not require this butt measurement, or else to subdivide 
the log by caliper measurements into shorter sections. Abnormal cross sections 
caused by limb swellings, or knots, should be measured, if possible, by taking the 
diameters at equal distances above and below the swelling. When logs are cut to 
small diameters in the top, the log may taper rapidly in the last few feet, and the 
disproportionally small diameter at the top will reduce the computed volume of the 
log as a whole. This problem may be solved by measuring the tapering portion 
separately as a short piece. In commercial scaling of logs which have abnormal 
diameters, the scaler should apply a measurement which in his judgment will give 
the correct contents of the log. 

In ordinaiy scaling, the diameter of logs is expressed in the nearest 
inch with fractions entirely dropped or rounded off (§83). For accu- 
rate volume measurements, each diameter is secured to the nearest 
tenth of an inch, for which purpose the rule or cahpers used must be 
graduated to tenths. In commercial practice, thickness of bark is never 
included in measuring the diameter of a log except when the bark is to 
be utilized, as for fuel or tannin,^ in which case the diameter is measured 
outside the bark. 

When the diameter of the log is taken in the middle, the thickness 
of bark must be ascertained and deducted. For accurate volume 
measurements, thickness of bark on one side may be determined by 
notching and measuring to the nearest tenth of an inch. Double this 
thickness when deducted gives diameter inside bark. Or the bark may 
be stripped from opposite faces in order to apply the calipers directly to 
the wood. This latter method is laborious and is seldom used even 
in scientific volume determination. 

26. The Form of Logs. Logs diminish in diameter from butt to 
top, corresponding to the form and growth of trees. This difference 
or loss in diameter at successive distances from the butt, is termed taper. 
The taper of logs gives them their characteristic foi'ms. On account 
of this taper, logs are never truly cylindrical no matter how closely 
they may approach the cylinder in form. 

The geometrical forms to which logs can be compared must there- 
fore be circular in cross section and tapering. The forms suitable for 
this purpose are the paraboloid, cone, and neiloid. 

1 Exceptions to this practice may be found in some regions, in scaling, when the 
log rule in use gives a large over-run which is offset by including width of one bark 

(§83). 



FOEMUL^ FOR SOLID CONTENTS OF LOGS 



19 



These three sohds form a series of successively diminishing per- 
centages of the volume of a cjdinder of equal basal area and height." 
Each tapers to zero at the tip. But logs are cut with two parallel 
faces at the two ends. The corresponding solids are the truncated 
forms of these bodies, termed frustums, as shown in Fig. 3. 




Fig. 3. — Forms of the cylinder, paraboloid, cone and neiloid, and truncated forms 
or frustums of the last three solids. 



27. Formulae for Solid Contents of Logs. The comparative vol- 
umes of these four solids are stated by formulae below; when 

5 = Area of base, square feet, 

6| = Area of cross-section, at | height, 

6 = Area of top, 

/i = Height or length, in feet. 



1 Each of these solids is formed by the revolution of a curve about a central axis. 

A true Appolonian paraboloid is derived from that form of a conic section (a 

symmetrical curve formed by the intersection of a plane with a cone) in which the 

plane is parallel with the side of the cone. For the conoid formed by the revolution 

of this curve about its axis, the ratio between a cross section taken at right angles 

with the axis at any point, and the height above this point to the apex, is constant 

Bh 
for all points on the axis. This gives a volume equal to — . Logs which taper 

regularly will have straight sides, and resemble a truncated cone. Logs whose taper 
is most rapid near the butt, diminishing towards the top, will have concave sides and 
resemble a truncated neiloid. The form and volume of such logs will usually fall 
somewhere between a neiloid and a cone. Most logs taper more rapidly at the top 
than at the butt and will have convex sides, and resemble in form a truncated para- 
boloid — -their volume usually falls between that of a paraboloid and a cone. Where 
most of the taper occurs close to the top, the log may exceed the paraboloid in volume, 
falling between it and the volume of the cylinder. 



20 



THE MEASUREMENT OF LOGS. CUBIC CONTENTS 



Form 


Volume of 
perfect solid 


Volume of Frustum 


Cylinder 
Paraboloid 

Cone 
Neiloid 


Bh 
Bh 
2 

Bh 

y 

Bh 

T 


Bh 

(B+b) h 

h, or {B-\-h) ^ . Smalian's Formula 

z z 

h\h. Huberts Formula 
(B+b+Vs-b)^ 

o 

h 
(B+Abh+b)-. Newton's Formula 
6 



Newton's formula will also give the volume of the cone, paraboloid 
and cylinder. 



The per cent of the volume of the cylinder which is contained in the other three 
forms, when of equal diameter at base and equal height, is 

Paraboloid 50 per cent 

Cone 33^ per cent 

Neiloid 25 per cent 

But each of these three solids decreases in cross section from base to tip, while that 
of a cylinder remains the same. The frustum of a cylinder is always a cylinder, 
while the frustum of a paraboloid, cone or neiloid with equal basal area tends to 
more nearly resemble a cyhnder as the area of its top section approaches that of 
its base, which results when the relative height of the frustum is shortened. The 
per cent of the cubic contents of a cylinder of equal base and height, which is con- 
tained in these frustums increases in the same manner, and the possible limits of 
variation in form and volume between the cylinder and each of the other three 
frustums correspondingly diminishes. 

E.g., when the height of the frustum is one-fourth that of the perfect solid, the 
per cent of cylindrical volume is, for 

Frustum of paraboloid 87 per cent 

Frustum of cone 77 per cent 

Frustum of neiloid Gl per cent 

When the height is one-eighth of a perfect solid, these per cents are: 

Frustum of paraboloid 94 per cent 

Frustum of cone 88 per cent 

Frustum of neiloid 77.5 per cent 

A rapidly tapering log forms a truncated section of a relatively shorter completed 
paraboloid or cone than a log with gradual taper. The greater the height of a com- 
plete paraboloid with a given basal area, the less it will taper for a given length, as 
16 feet. Whether the taper is rapid or gradual, a log may exactly resemble the 
frustum of a paraboloid, cone, or neiloid, 



RELATIVE ACCURACY OF SMALIAN AND HUBER FORMULA 21 

Provided it has the true form of one of these soHds, its volume can be exactly 
determined by employing the corresponding formula. But the true form of the 
log may fall anywhere between the fixed points or forms in the series, which are 
marked successively by paraboloid, cone and neiloid, and in this case the volume 
even when calculated by the formula which corresponds most nearly to its Lrue 
form, will still be in error by the amount of this divergence. This error may be 
excessive for long logs. 

But by taking advantage of the effect of reducing the proportional height of the 
frustum, the probable error from this source may be reduced to any desired limit of 
accuracy. This is done simply by shortening the length of the logs, or by dividing 
each log into several shorter sections, measured separately. It is then no longer 
necessary to employ two or more forms arbitrarily according to the variations in 
the form of the logs, but a single standard geometric form may be chosen, which 
most nearly resembles the average form of logs, and the same formula? applied to all 
logs measured. 

The paraboloid comes nearest to answering this requirement, and for this reason 
the Smalian formula and the Huber formula have been generally adopted for both 
scientific and practical measurements of cubic volume of logs, to the exclusion of 
the formula? for cone and neiloid. 

28. Relative Accuracy of the Smalian and the Huber Formulae. 
Logs having the form of a truncated paraboloid are measured with 
absolute accuracy regardless of their taper by either Ruber's or Smalian's 
formula. But if the form of the log is more convex and lies between 
that of the paraboloid and the cylinder, the Smalian formula, measur- 
ing the two ends, gives too small a result, while the Huber formula will 
give too large a volume. Nearly all logs lie between the frustum 
of a paraboloid and the frustum of a cone in form, having slightly 
convex sides, but not the full form of the paraboloid, so the end area 
formula (Smalian's) shows an excess, while the middle area measurement 
(Huber's) gives too small a result. In either of the above cases, 
the error by Huber's formula is one-half that of Smalian's and opposite 
in character. 

Newton's or Prismoidal Formula. To check the accuracy of measure- 
ments made on sections of given length and to determine the maximum 
length of section which will secure the desired degree of accuracy, the 
prismoidal formula may be applied. This formula is correct for cylinder, 
paraboloid, cone or neiloid, and consequently for logs of regular form 
whose volume lies within these extremes. It will not measure accu- 
rately eccentric or. distorted forms resembling none of the above solids. 
The formula requires the measurement of both ends and the middle 
section, and is known as Newton's formula. 

When the form of logs resembles more closely the cylinder, cone or 



22 THE MEASUREMENT OF LOGS. CUBIC CONTENTS 

neiloid than the paraboloid, the errors in the use of the Huber or the 
Smahan formula may easily be checked by the above formula.^ 

29. The Technic of Measuring Logs. By either of the two para- 
boloidal formulae, Ruber's or Smalian's, the area of a single average 
cross-section is obtained which, multiplied by the length of log, gives 
the cubic contents. By the Smalian method, this area is the average 
of two cross-sections, while by the Huber method it is obtained directly. 
The volume of the frustum, or log, is thus equal to that of a cylinder 
of equal height, with a base equal in diameter to the average cross- 
section. 

Diameters Measured at Ends of Log. Diameter inside the bark is 
usually required, and is best obtained at the exposed ends of the log. 
But if only the small end is measured, the corresponding cylinder 
does not give the cubic contents of the log on account of neglect of its 
taper (§ 26). Although almost universally practiced in scaling for 
board feet, this single measurement is never used to scale cubic contents. 
The choice lies, therefore, between the single measurement at middle 
of log, or the averaging of two end areas. 

The volumes of cylinders vary directly as their basal areas, or as D^, and not as 
their diameters. Hence an accurate procedure would require first, measurement 
of each diameter; second, determination of each corresponding area; third, averag- 
ing these areas; fourth, computing the corresponding diameter. The volume of a 
cylinder of this diameter and length is required. Such a procedure is practical only 
in scientific studies; in scaling, the two end-diameters are averaged directly. The 
assumption is that, 

1 The following formulae are cited by Guttenberg, in Lorey's Handbuch der 
Forstwissenschaft, 3d Ed., Chapter XII, 1913. 



Breymann, 


V=\{B+b+2,h\+hl) 
o 


Hossfeld, 


F=^(36i+6). 
4 


Simoney, 


V = ^(2(h\+h\)-hh). 



While the substitution of the Hossfeld formulae for that of Smalian on butt logs 
would give far more accurate results, and would be closer than the Huber formula, 
the point one-third from butt is not ordinarily measured in the field and is trouble- 
some to ascertain. Hence this formula is impractical. The same objection applies 
to Breymann's. Simoney's formula has no advantage over either Huber's or 
Smalian's, since by using the small lengths, one-fourth log, the latter formulae will 
secure results within 1 per cent of the true volume for the standard 16-feet length. 



THE TECHNIC OF MEASURING LOGS 23 

This gives a slightly smaller volume than by the correct method. The error increases 
as the square of the difference between the top and the bottom diameters. • 

This error, expressed in per cent of total contents, falls below 1 per cent for logs 
not over 16 feet long with a taper of 2 inches or less. It also tends to offset the plus 
error caused by the use of the Smalian method as a whole ( § 28) . The error increases 
with length of log scaled as one piece. 

A far more serious source of error by this method is that due to the flare of butt 
logs. Due to the excessively large cross-section thus obtained at the butt, this 
error may give an excess cubic volume for the log of from 10 to 20 per cent. Chiefly 
for this reason, the end area method is confined in practice to scientific studies of 
volume, in which the length of the sections can be regulated to reduce this error, 
and time is not the determining factor. For such studies, the computation of average 
basal areas is no drawback. The volumes of the lengths into which the log is to be 
divided are more conveniently computed by the Smalian formula than by the Huber 
formula, which requires the middle diameter of each short section. Smalian's 
mean end formula is therefore universally adoi)ted in these studies, 

Diameter Measured at Middle of Log. Since it is impossible to 
measure the diameter at the middle of a log unless the log is exposed, 
logs cannot be scaled by this method if they lie in large rollways or 
piled one on another. The scaling for cubic contents therefore requires 
a time and place for the work where each log is exposed for its entire 
length and is less convenient than scaling for board feet ( § 83) . 

By measuring the middle diameter, the error due to flaring butts 
is avoided. But this practice requires, in addition to total length, 
the determination of this middle point. The use of calipers is required, 
since it is impossible to obtain consistent accuracy by placing a scale 
stick across a log and judging the diameter; the error thus incurred 
is always minus. This method is therefore termed a caliper scale. 

In applying a caliper scale, the double width of bark is subtracted 
either by taking off a fixed average thickness or bj^ adjusting the calipers 

1 The error in use of mean diameters is shown as follows: 
Volume of truncated cone may be expressed as, 

V = ^JiiD-'+Dd+d''). 

Volume of cylinder having a basal area equal to the mean diameter of the log is, 

4 2 
Then, 



12 4 2 12 2 ■ 

The minus error thus shown is equivalent to the volume of a cone having a basal 
area equal to the difference between the mean end diameters of the log. For the 
paraboloid, this error equals the contents of a cylinder with a basal area equal to 
that of the above cone. The error thus increases with the total taper of the log. 



24 THE MEASUREMENT OF LOGS. CUBIC CONTENTS 

to read that much less in diameter for all logs alike. For more accurate 
scaling the width of bark is deducted separately for each log. 

The caliper scale is the more accurate of the two methods for 
commercial use. The volumes by this formula, in average logs, are 
slightly below the actual contents.^ 

Where the length of a log exceeds that which can be accurately 
measured as one log by the above methods, the practice is to consider 
it as composed of two or more shorter sections. By Smalian's method, 
the intermediate points measured are taken as the ends of these sec- 
tions. By Ruber's method, the middle point of each section is found. 
In either case, calipers should be used. The length of section which 
can be measured without subdivision depends primarily on the rapidity 
of taper. Logs or sections whose total taper does not exceed 2 inches 
may be scaled or measured as one piece regardless of length. In com- 
mercial scaling logs less than 18 feet long are seldom subdivided. In 
scientific studies 8 feet is usually the maximum length between measure- 
ments of diameter, and 4 feet is often required for the first or butt 
sections. 

30. Girth as a Substitute for Diameter in Log Measurements. 
The circumference of tlie circle, corresponding to the girth of the log, 
may be used to determine the area of the cross-section.- In this case, 
if (7 = girth, and B = Basal or end area, 

47r 

A tape is used in which the results are read directly in inches of 
diameter, each inch being equal to 3.1416 inches on the tape. A pin 
in the end of the tape enables one man to encircle the log. 

The ratio between diameter and circumference, tt, holds good only 
for the circle. The more eccentric the cross-section, the greater this 
ratio becomes, and the smaller the actual area in proportion to girth. 
Hence, whatever error occurs by this method tends to give a cross- 
sectional area greater than the actual area.'^ 

1 Tests of 4398 spruce and fir logs measured in lengths up to 40 feet by this method 
in Maine indicated that the scale required a correction factor of 1.049 or 4.9 per cent 
over-run. The Measurement of Logs, Halbert S. Robinson, Bangor, Me., 1909. 

2 Girth measurements are commonly used in India, and in commercial measure- 
ment of imported logs in England. In the United States, the girth of large logs is 
sometimes taken, when more convenient than the measurement of diameter, but 

G 

the result is reduced to diameter by the formula D = — = .3183G. 

TT 

' Mensuration of Timber and Timber Crops, P. J. Carter, Office of Supt. of 
Gov't. Printing, Calcutta, 1893, p. 2. 



GIRTH AS A SUBSTITUTE FOR DIAMETER 25 

One advantage of giith measurements over diameter is that two 
measurements taken at the same point give consistent results, while 
in determining the average diameter of large and irregular or eccentric 
logs, considerable differences may occur in two separate measurements. 
Owing to the difficulty of measuring the girth of a log at its middle 
point, the mean of the two ends may be taken. This incurs an error 
identical with that by the mean diameter method (§29). This error 
is offset by the tendency of .girth measurement to over-run. 

The volume of the cylinder whose basal area is obtained from girth 
may be found by the method of the Fifth Girth in which 

G is here expressed in feet. If measured in inches, divide the result 
by 144. Another method, known as the Quarter Girth, is expressed as 

F=(f)\.113. 

In this formula G is expressed in inches.^ 

1 The Fifth Girth method will give a result which is only approximately correct. 

G=irD, 



—— n should equal I — I 2/i, 



therefore, 



and 

— should equal ( I X2, 
4 \5/ 

.7854 should equal .6283= X2, 

.7854 should equal .7895, 

an error of less than 1 per cent. 

The Quarter Girth formula is of no particular value as it is merely a means of 
correcting a commercial standard ( § 35 Hoppus or Quarter Girth Log Rule) to 
obtain the full volume of the cylinder. 



CHAPTER IV 
LOG RULES BASED ON CUBIC CONTENTS 

31. Comparison of Log Rules Based on Diameter at Middle and 
at Small End of Log. Log rules giving the contents of logs in cubic 
feet should be based on the diameter inside bark at middle of log. If, 
instead, the diameter is measured at the small end of the log, the indi- 
cated contents falls short of the true cubic volume (§ 29). 

But the measurement of diameters at the small end of logs rather 
than at the middle point is so great a convenience in log scaling ( § 83) 
that efforts have been made to find a converting factor, or ratio, by 
which the true contents of logs may be correlated with diameters at 
the small end, and expressed directly in a log rule based on these diam- 
eters. Since the true contents is assumed to be equal to the cylinder 
whose diameter is that of the log at its middle point, the ratio or factor 
desired is the multiple required for converting the volume of the smaller 
cylinder whose diameter is measured at the small end of the log into 
the true cubic volume of the log taken as equaling this large cylinder. 
This ratio is influenced by three factors— namely, rate of taper, length, 
and diameter of the log. 

A log rule, if based on the same conversion factor for logs of all sizes and tapers, 
will give correct volumes only for a log of a given diameter, length and taper and 
will be in error for logs of all other dimensions, 

A log rule based on separate conversion factors for logs of each diameter but 
making no further distinction for different lengths or tapers will give correct volumes 
only for logs of a specific length and rate of taper in each diameter class, and will 
be in error for all other lengths and tapers. 

A log rule based on separate conversion factors for each different diameter and 
length, can be applied accurately to obtain the average scale of logs of all diameters 
and lengths only in case the average taper of the logs scaled agrees with that of the 
logs measured in determining the factor used, and is in error when the average 
taper of the logs scaled is greater or less than this. 

While these conditions apply to log rules based on measurement at the small end 
of log, a log rule based on measurement at middle of log is correct for all the above 
conditions, incurring only the errors due to divergence in shape of log from that of 
a paraboloid. 

The ratio of volumes, and the loss in scaling legs by a rule based on the cylinder 
measured at small end, are illustrated in Table I. The figures in the last column 
represent the loss in scale expressed in per cent of the volume scaled, e.g., a 16-foot 
log 6 inches at the small end with 2-inch taper contains 36 per cent greater volume 
than shown by the scale. 

26 



COMPARISON OF LOG RULES BASED ON DIAMETER 



27 



a 

>j 
ij 
■< 

s 
m 

< 

Q 
< 

a 


Over-run. 
Per cent 


(N CO ^ ^ t^ 


COi-fCOCMt^ 


COtI CO CM t> 


t^cOCMO-* 


COI>rH00CO 
CCrHr-t 


l>COfOt^CO 

t>.OOCM.-H rH 


i> CO CO t^ CO 

!>• CO C<l --H r-l 


t>.t>.C5CDQ0 
I>|>TJHC0CM 


Proportion 

of total 

contents 

scaled. 

Per cent 


Tt<(Nt^(Mt^ 


CO lO --1 CO 05 


C0>0 --I CO c» 


O COO lO 05 


fO>0 05(M CO 
t>. GO 00 0105 


CO CO --no t^ 
k01> 00 00 00 


COCOt-i lO t^ 
1CI>00 00 00 


CO CO t^ CO t-- 
COuOCOt^l^ 


Loss in cubic con- 
tents. 


CI 


O GO CO 00 CO 


l> lO 05 t>- i— 1 


1> IC CS t>. i-H 


O b- O IC tH 




coco OOTfHCM 

Ttl CM T-H T-H T-H 


CO CD 00^ CM 

■* CM T-H .-1 r-H 


"* CO cocoes 

COTjiCOCMCM 


Id 


■* 00COt^(M 
^ ^ CM C<) CO 


o> 00 CO ic ■* 

OOOCM Tt< CO 


»OC0 rf CM CM 

•^ lO CD t^ 00 


t^ CO CM O 00 

^ >oo5co CO 


.-H(N COrtH lO 




CMrfcOOOO 


-H 05 t^ CO ^ 
^ ^ CM CO '*< 


H 
<1 
Q 
H 
iJ 
<) 
O 

m 

03 
H 

o 
O 
o 
m 

O 


Middle. 
Cubic feet 


C^I>iOiO00 


t^rH^HOOCM 

>-HCM00O5I> 


O O .-H 05 CD 
lOrH © OCO 


lOOO t^ CO CO 
Tt< CD T}H oot^ 


rjl TjH .-(•>!*< CO 
tHCOiOOO 


i-HrtH Oit^ 00 
T-H CO COi-H t^ 


lOt^-"* 00 Oi 
tH CO lO 00 


t>- •* 'J^ CO T-H 

T-ITJH oocoo 
.-iCM 


Small 
end. 

Cubic feet 




CO CO lO CO 00 
CM T-H iO O O 


.-HiOCMCMiC 


00 CO lO CO 00 
CMt-HOiO c 


COIM OOO CO 


coiocoot^ 

CM lOOiO 

I— 1 1-H 


CO CM 00 O 00' 
i-H CM »C t^ 


CO lOcO o t^ 
CM lO C "O 


Diameter 

at 

middle 

of 

log. 

Inches 


t^ CO 05 lO ^ 
^ ^ CM CO 


00t)< O COCM 
^CM CMCO 


00 --^O CD CM 
--H CM CM CO 


OCOCM OOTfH 
■-I —1 CM CM CO 


Diameter 

at 

small 

end. 

Inches 


CD CM 00 ■* O 

-H rH CM CO 


CO CM 00 "*0 

^r-lCM CO 


CO CM 00 '^ O 
^^CMCO 


CD CM 00-* O 
>-• >-i CM CO 


Total 
taper. 

Inches 


C^l 


'I* 


'^ 


GO 


Taper 

per 
16-foot 
length. 

Inches 


CM 


CM 


■^ 


■* 




Length 
of 
log. 




CO 


CM 

CO 


CD 


CM 

CO 



28 LOG RULES BASED ON CUBIC CONTENTS 

Table I indicates that the per cent of error resulting from assuming that the total 
contents of a log is equal to that of the cylinder measured at the small end decreases 
with increased diameter, increases with the total number of inches of taper in the 
log but for logs with a given diameter and the same number of inches of total taper, 
the per cent of error is the same regardless of the rate of taper or length of log, and is 
determined by the difference in volume of the cylinders based respectively on diameter 
at small end and middle of log. 

32. Log Rules in Use, Based on Cubic Volume. There are two 
classes of log rules in use, based on cubic volume. The first class gives 
the actual or total cubic contents of the log. The second class gives 
the volume of sawed lumber expressed in board feet, but these rules 
are based upon the use of a fixed ratio of conversion from cubic volume 
and not upon the volume of sawed lumber which can actually be obtained 
from logs of different sizes (§ 39). 

Cubic measure was early adopted in log measurements, but owing 
to the fact that logs are roughly cylindrical in shape, the custom grew 
up of using the contents of a cylinder of standard dimensions instead 
of the simpler standard of the cubic foot. There is no advantage in 
this substitution of new arbitrary cubic standards for the cubic foot.^ 

The principle used in the application of such a standard ^s that the 
volumes of cylinders of different sizes will vary as the square of the 
diameter multiplied by the length. The contents of all logs can then 
be expressed in a log rule in terms of the number of standards they 
contain. 

The Adirondack Standard, or Market. In the Adirondack region 
of New York several such standards have been used but the only one 
of importance is the 19-inch or Glens Falls Standard, termed also the 
Market.^ This is a cylinder 19 inches in diameter and 13 feet long, 

1 The cubic meter is the standard of volume used in the Philippine Islands. 
Logs less than 8 meters (26j feet) long are measured as a cylinder whose diameter 
is the small end. The average diameter in centimeters is taken, the end area is 
obtained from tables and multiplied by the length of the log in meters to give the 
volume in cubic meters. For logs over 8 meters in length, the diameter at the middle 
is taken, or if this is impractical, the average of the diameters of the two ends is used. 

2 It is assumed that one market equals 200 board feet which is 65.1 per cent of 
its cubic contents regarding the log as a cylinder measured at the small end of log 
and neglecting taper. This gives 7.8 board feet per cubic foot. 

Tests of actual output in board feet per market, sawed from 600 logs of each sepa- 
rate diameter, gave the results as shown in table on opposite page. 

The saws used were a band and a band resaw, both cutting i^-inch kerf. The 
lumber was 60 per cent 1-inch, the rest Ij-inch and 2-inch thicknesses. These 
ratios are therefore higher than for inch lumber sawed with j-inch kerf. The ratio 
is still further increased by the fact that the cubic contents measured does not include 
the entire log but only the cyhnder measured at small end while the sawed output 
is from the entire log. H. L. Churchill, Finch, Pruyn Co., Glens Falls, N. Y. 

Twenty-two-inch Standard, A different unit is in use to a slight extent 



LOG RULES IN USE, BASED ON CUBIC VOLUME 



29 



equivalent to 25.6 cubic feet. In application the log is measured at 
the small end and its contents are taken as that of the corresponding 

small cylinder. The taper is disregarded. 

* 
When Z) = diameter of standard log in feet or in inches; 
L ^ length of standard log in feet. 

The volume of the standard is .7854 D'^L. 

Let d and I equal the diameter and length of any other log, whose 
volume will be .7854 dH. 

The volume of any log is found in terms of standard units by the 
formula, 

J854dH__m_ 

.7854D2L~^' 



F = 



The market is still a common standard of log measure on the 
Hudson River watershed in the Adirondack region. 

Its neglect of the taper makes the Adirondack standard unsuitable 
for measurement of pulp wood, but were it applied at middle of log 

on the Saranac river drainage in New York, termed the Twenty-Two-Inch Standard. 
The standard log is here 22 inches at small end, and 12 feet long, containing 3L68 
cubic feet. It is assumed that one standard equals 250 board feet which equals 
65.8 per cent of the cubic contents of the small cylinder. There have been still other 
log standards, which are now obsolete. 



Diameter at 


Board feet 


Board feet 


Diameter at 


Board feet 


Board feet 


small end 


per 


per 


small end 


per 


per 


inside bark. 


market 


cubic foot 


inside bark. 


market 


cubic foot 


Inches 






Inches 






5 


1.35 


5.3 


13 


228 


8.9 


6 


155 


6.0 


14 


236 


9.2 


7 


168 


6.6 


15 


243 


9.5 


8 


179 


7.0 


16 


248 


9.7 


9 


190 


7.4 


17 


252 


9.8 


10 


200 


7.8 


18 


255 


9.9 


11 


210 


8.2 


19 . 


257 


10.0 


12 


219 


8.5 


20 


259 


10.1 



In principle and practice, these standards coincide closely with the use of the 

cubic meter, the only difference being in the size or cubic contents of the unit. The 

difference in shape, or use of a cylinder instead of a cubic foot, is of no significance. 

Since the cubic meter contains 35.3156 cubic feet, the market is a smaller standard. 

The cubic volumes are convertible from one of these standards to another by using 

25.6 
the proper ratios; markets to cubic meters - — — - = .725; markets to cubic feet 25.6. 

35.31 



30 LOG RULES BASED ON CUBIC CONTENTS 

it would give accurate contents. This standard, in common with all 
other cubic rules, is unsuited to the measurement of the board foot con- 
tents of logs. 

33. The Blodgett or New Hampshire Cubic Foot. A cylindrical 
unit has been adopted as the legal standard of the state of New Hamp- 
shire. The statute reads, " All round timber shall be measured accord- 
ing to the following rule. A stick of timber 16 inches in diameter and 
12 inches in length shall constitute 1 cubic foot; and in the same ratio 
for any other size and quantity." This arbitrary cubic foot contains 
1.396 or approximately 1.4 cubic feet. 

The contents of logs is computed in Blodgett feet by the formula, 

This log rule is based on the middle diameter, and is therefore more 
accurate in application than the Adirondack standards. The diameter 
is measured by calipers and double width of bark is deducted (§ 84). 

This rule is a rough attempt to use the cubic foot, with an allowance for waste 
in squaring round logs. But the per cent of waste by the rule is 28.4 per cent of the 
cylinder, utilizing 71.6 per cent, while the area of an inscribed square is 63.6 per 
cent of the circle with 36.4 per cent waste. The "squared" stick 1 foot long would 
therefore have considerable wane. The Blodgett Rule was an attempt to secure a 
standard which could be converted into board feet. The statute fixed the converting 
factor as, 

100 Blodgett feet = 1000 board feet, or a ratio of 1 : 10 

But in scaling practice it was concluded that this ratio was unsatisfactory, and 
gave too large a scale in board feet. So it was arbitrarily set in practice at 

115 Blodgett feet = 1000 board feet, or a ratio of 1 :8.7, 

when the rule was applied, as intended, to the middle diameter inside bark. Though 
the scale in Blodgett feet in either case was the same, the converted resalt gave for 
the ratio of 1 : 10, 59.7 per cent of the contents of the log in board feet, and for the 
ratio 1 : 8.7, 51.9 per cent. Since 12 board feet = l cubic foot, 

10 

= 83g per cent of 1 cubic foot. 



12 



and 



Likewise, 



and 



1 


.831 
.396 


=.597. 








8.7 
12 " 


= 72.5 


per 


cent. 




.725 


= 519. 







1.396 



USE OF CUBIC FOOT IN LOG SCALING 



31 



In order to permit measurement of diameter at the small end of log instead of 
the middle (§31), a further modification of the rule more radical in its character 
was now made. The loss in cubic contents by measuring the small cylinder was 
offset by arbitrarily increasing the ratio of board feet to each Blodgett foot. This 
new ratio was set for logs of all sizes at 

106 Blodgett feet = 1000 board feet. 

When compared with the cubic contents of the sinall cylinder this makes the ratio 
1 : 9.44. For the ratio of 1 : 9.44 the per cent of the small cylinder scaled as boards 
is 56.2 per cent. But for the true cubic contents of the log the ratio would vary 
with length and taper of log ( § 31) . 

9.44 
12 " 



■ 78f 
1 396 



= 56.2 per cent. 



From Table I, § 31, the following comparisons can be made between the volume 
thus expressed and the true volume. Taking 16-foot logs with 2-inch taper, 



Diameter 

of 

log. 

Inches 


Per cent of total con- 
tents of log in small 
cylinder 


Per cent of total con- 
tents scaled as boards 
by above ratio of 
56.2 per cent. 
Per cent 


6 
12 
18 
24 
30 


73.4 
85.2 
89.7 
92.2 
93.7 


41 2 
47.8 
50.4 
51.8 
52.6 



The attempt to convert this rule to apply at small end gives values which agree 

with the current ratio of 115 Blodgett feet to 1000 board feet in 16-foot only when 

these logs are 24 inches in diameter and with 2-inch total taper, while for 6-inch logs, 

41.2 
tapering 2 inches the scale is or 79 . 3 per cent, incurring a loss of 20 . 7 per cent 

51.9 

of the true cubic scale measured at the middle point. 

Thus the change in point of measurement destroys the consistency of this log 

rule for cubic contents, while the conversion to board feet introduces still another 

error, discussed in § 42. The rule should either be used for Blodgett feet only, as a 

cubic measure, and applied only at middle diameter, or if the end diameter is used, 

the conversion factor should have been separately computed for logs of different 

diameters and lengths on basis of an average taper. 

34. Use of Cubic Foot in Log Scaling. The cubic foot has been 
substituted for the Blodgett foot as the basis for measuring logs, by 
the U. S. Forest Service on the National Forests in Maine and New 
Hampshire. 



32 



LOG RULES BASED ON CUBIC CONTENTS 



A caliper with a long arm to the end of which is attached a measuring wheel, is 
used. The wheel consists of ten spokes, each tipped with a spike, and all painted 
black except one, which is yellow. The tips of the spokes are 6 inches apart. The 
yellow spoke is weighted. When the wheel is run along a log, each revolution as 
comited by the yellow spoke measures 5 feet, and the remaining spokes permit the 
length of log to be measured to the nearest 6 inches. The measuring wheel is run 
the length of the log, and then brought back to the center, at which point the caliper 
measurement is taken. Allowance for bark is made by moving the caliper jaw 
inward by a distance in inches equal to the estimated double width of bark on each 
log separately. 

The diameter in inches is stamped on one edge of the arm, and around the base 
of the arm are placed standard lengths running from 8 to 34 feet. Opi)osite each 
length, and below each diameter, on the arm, is stamped the cubic volume of a log 
of these dimensions. The lengths are also stamped on the movable arm. When 
the log is caUpered, the scaler reads the volume which lies opposite the proper length, 




Fkj. 4. — Caliper scale for measuring logs in middle, outside bark, with wheel for 
determining length of log. 



the diameter being indicated by the position of the movable arm after calipering the 
log and taking off the bark correction. Defects are then deducted from the gross 
volume, either by measuring the defective portion or by ocular estimate of the volume 
of the defect. J. J. Fritz, Gorham, N. H., 192L 

Note. In 1909 a commission of investigation recommended to the Maine 
Legislature the adoption of the cubic foot as the statute rule of Maine. This was 
not done. One lumber company, Hollingsworth & Whitney, Waterville, Maine, 
has since 1904 used a cubic foot standard, measuring the middle diameter with caU- 
pers, outside bark. The rule then allows 12^ per cent deduction for volume of bark, 
and gives the net cubic contents of solid wood. The per cent of volume of bark is 
not constant but varies with the size of tree and its age and exposure. The arbitrary 
figure chosen simply represented the approximate average volume for the species 
and region in question, namely, spruce and balsam in Maine. 

A converting factor for this rule has been suggested, of 185 cubic feet to 1000 
feet B. M. This gives 5.4 board feet per cubic foot, or 45 per cent of the cubic con- 
tents when measured at the middle. Reduced to diameter at small end, for a taper 
of 1 inch in 8 feet, logs 18 inches in diameter would give 50 per cent of the small 



LOG RULES FOR CUBIC CONTENTS OF SQUARED TIMBERS 33 

cylinder in board feet. This suggested ratio is therefore lower than those adopted 
for the New Hampshire and most other converted cubic log rules. 

Note. Weight as a Basis for Measuring Cubic Contents. Actual weight of logs 
is seldom used as a basis of measurement, as the variation in moisture contents 
caused by seasoning prevents standardization even for a given species. A few 
valuable timbers are imported by weight. The long ton of 2240 pounds is used. 

The ton as ordinarily used in measuring timber is a cubic measure equivalent to 
either 40 or to 50 cubic feet and is usually applied to squared timbers. The unit of 
50 cubic feet is also termed a "load" and is used in measuring teak. 

Red cedar logs are sometimes purchased by weight, on account of their extreme 
irregularity and the difficulty of measuring them. 

35. Log Rules for Cubic Contents of Squared Timbers. A definite 
departure from the use of total cubic contents is found in log rules 
giving the cubic contents of the squared timbers which may be hewn 
or sawed from round logs. The waste constitutes the portion hewn 
or slabbed off. A square inscribed in a circle occupies 63.6 per cent 
of its area. Rules based on this principle would give a waste factor 
of 36.4 per cent of the cylinder scaled. 

Inscribed Square Rule. The width of a square inscribed in a 24-inch 
circle is 17 inches.^ The width of any other inscribed s(juare is seven- 
teen twenty-fourths of the diameter of the log. The cubic contents 
of the log is that of the square so determined, measured at the small 
end of log. 

The width of a square inscribed in a 17-inch circle is 12 inches, each 
foot of log containing 1 cubic foot of squared timber. The cubic con- 

tents of anv log is --=o-^- Bv either of these rules of thumb, the so-called 
17*^ 

Inscribed Square Rule is obtained. The latter method is termed the 
Seventeen- 1 rich Rule. The rule gives 63.4 per cent of the cubic contents 
of the small cylinder, and proportionately less of the entire log depend- 
ing on taper, length and diameter (§31). 

Big Sandy Cube Rule. Synonyms: Cube Rule, Goble Rule. This 
Cube Rule, used on the Ohio River, assumes that it requires a log 18 
inches in diameter at small end to give a timber 1 foot square. This 
rule scales 56.6 per cent of the small cylinder. The volume of logs of 
other sizes is found by the formula, 

jr)2 
V = — L 

This rule is sometimes expressed in board feet by multiplying the 
cubic contents by 12. 

1 The side of the inscribed square is found by squaring the diameter of the log, 
dividing by 2 and extracting the square root, 



34 LOG RULES BASED ON CUBIC CONTENTS 

Two-thirds Rule. By this rule, the diameter of the log is reduced 
one-third, the remainder squared, and multiplied by the length of the 
log. As diameters are in inches the formula is F = (fZ))^ L^-144. 
This is a caliper rule applied to the middle area, and gives 56.5 per 
cent of the full cubic contents of the log. It is sometimes erroneously 
applied to the small end. 

Quarter Girth or Hoppus Rule. This rule depends upon the direct 
use of the girth, rather than diameter. The average girth is taken 

in inches at middle point, or by averaging both ends. Then V "={-7) L. 

This formula gives 78.5 per cent of the actual total cubic contents of 
the log. It is a commonly used standard for measuring round logs in 
England and India. To express the contents in cubic feet the result 
is divided by 144. 

36. Log Rules Expressed in Board Feet but Based Directly upon 
Cubic Contents. The Blodgett or New Hampshire rule is not the only 
log rule based on cubic contents, which attempted to express the results 
in terms of board feet. Any cubic rule can be converted into board- 
foot form, in theory, by the use of a ratio similar to those used for the 
Blodgett Rule. The ratio for board-foot contents of one cubic foot is 12. 
Twelve 1-inch boards cannot be sawed from 1 cubic foot, but a squared 
timber 12 by 12 inches contains 12 board feet per linear foot. For con- 
verting the entire log directly into board-foot contents of squared 
timbers, it is evident that the ratio will be less than 12 board feet per 
cubic foot, due to waste in squaring the log, while the conversion into 
contents in inch lumber requires a still lower ratio. 

The characteristic of all converted rules is that a fixed multiple 
or converting factor is used, regardless of the diameter or taper of 
the log. The rules differ only in the converting factor used, and in 
the method of measuring the log, whether at middle, or end. 

Constantine Log Rule. This rule is merely the expression of the cubic 
contents of a log regarded as a cylinder, in terms of board feet, by 
multiplying the cubic contents by 12. The diameter is measured at 
the small end of log. The formula is 

,. 7rZ)2 



4X144 



The rule is used to measure the contents of logs used for veneers. 

Cuban One-fifth Rule. This Rule is based on the square of one- 
fifth of the girth taken in middle of log. The formula when G is in 
inches is 



FORMULA FOR BOARD-FOOT RULES 35 

The rule gives just 50 per cent of the total cubic contents of logs 
in board feet. This is equivalent to 6 board feet per cubic foot. This 
rule is extensively used for imported hardwood logs. The contents 
of logs in cubic feet is found by dividing bv 144 instead of 12. 

In practice, fractional inches resulting from the fifth girth are dropped as follows, 
e.g., 

Girth, .50, 51 or 52 inches Square, 10 bj' 10 inches 

53, 54 inches 11 by 10 inches 

55, 56, 57 inches 11 by 11 inches 

58, 59 inches 12 by 11 inches, etc. 

Square of Two-thirds Rule. Sj^nonyms: St. Louis Hardwood, 
Two-Thirds, Tennessee River, Lehigh, Miner. This rule is derived from 
the Two-thirds Rule by multiplying the cubic scale by 12. The rule 
is used for hardwood logs in the Middle States, and for pine to some 
extent in the South Atlantic States, and is frequently erroneously 
applied to the small-end diameter of the log. 

Cumberland River Ride. Synonyms: Evansville, Third and Fifth. 
This rule resembles the Square of Two-Thirds Rule, in that one-third 
of the diameter is deducted and the remainder squared. But it differs, in 
that one-fifth of the volume of the squared stick is then subtracted for 
saw kerf, and the remainder converted into board feet. The rule is 
always applied to the small end of the log except for long logs, when 
the diameter at middle point is taken. This rule is used on the Missis- 
sippi Valle}^ and its tributaries, for hardwood logs. 

Square of Three-fourths Rule. Synonyms: Portland, Noble & 
Cooley, Cook, Crooked River, Lumberman's. In this rule, one-fourth 
is deducted from the diameter at small end, and the squared timber 
expressed in board feet. The rule was formerly used in New England 
but is now obsolete. 

Vermont Rule. This rule is derived from the Inscribed Square 
Rule by multiplying the values by 12. It is the legal standard of the 
State of Vermont. The contents of a 12-foot log may be calculated by 
a rule of thumb, by multiplying the average diameter of the top of the 
log inside bark, in inches, by half such diameter in inches. The rule is 
not extensively used even in Vermont, being supplanted by others, 
notably the New Hampshire or Blodgett Rule. 

37. Formula for Board-foot Rules Based on Cubic Contents. 
Any board-foot log rule the values for which are obtained by deducting 
the same per cent from the cubic contents of logs of all sizes, may be 
expressed by the formula 

Board feet = (1 - C)^ X ^ X L, 
4 144 



36 LOG RULES BASED ON CUBIC CONTENTS 

in which C = total per cent of waste deducted from the cyHnder, 
1 — C = per cent of cubic contents utiHzed, 

— j-7 reduces D'~ from inches to square feet, and 
144 ^ ' 

12 converts cubic feet to board measure. 
The formula, simplified, becomes 

Board feet =(1-C)^L. 
4o 

But the important distinction remains, that some of these log rules 
are meant to apply to the middle diameter and others to the small end, 
and while the per cent subtracted from the cylinder measured is uniform 
for the rule, the per cent actually subtracted from the log is uniform only 
for those rules using middle diameter, and varies over a wide range for 
rules based on diameter at small end of log. 

Note. Obsolete Rules. The following log rules, obsolete or unused, are based 
on the above formula and principles: Saco River (Maine), Derby (Mass.), Partridge 
(Mass.), Stillwell's Vade Mecum (Ga.), Ake (Pa.), Orange River or Ochultree 
(Texas). A new rule, the Calcasieu (La.), deserves the same fate. The Tatarian 
rule (Wis.), which is based on this principle, gives approximately correct board- 
foot contents for a log of a given size. It has never been adopted in practice. 

38. Comparison of Scaled Cubic Contents by Different Log Rules. 

In Table II is shown the comparative volumes, in per cent of total cubic 
contents, which are scaled by different log rules based upon cubic 
volume. These per cents represent the converting factor used to obtain 
the values given in the rule from the volumes of cjdinders. 

Note. The values in this table were obtained by applying the ratio between 
the volume of two cylinders 16 feet long, IS inches and 19 inches in diameter respect- 
ively. This ratio is 28.27 : 31.50. Log rules based on cylinder at small end then 

28.27 

scale but • or 89.7 per cent of their volume, to which the reduction per cent for 

31.50 ' 

waste is applied; e.g., the Vermont rule wastes 36.6 per cent by the inscribed square 

method. Then, based on the small end, the per cent scaled is 63.4, but based on 

middle diameter for the above size, it is 89.7X63.4 = 56.9 per cent. The table gives 

a correct comparison of the different log rules which are constructed by using a 

fixed per cent of cubic volume. The per cents given for the rule under the first 

column, based on the point at which the rule is applied, are consistent for all logs. 

But the equivalent per cents obtained by converting the scaled contents into terms 

of the cylinder based on the other diameter — as middle, for logs measured at the end 

and vice versa, will vary as the relative contents of these two cylinders varies (§ 31). 

This will not change the rank or order in which the rules fall. The rules are tabulated 

in order of the relative per cent of total contents which they scale. 

There is no common standard for measuring the cubic contents of squared timbers. 

The Quarter Girth method gives the tullest measurements, while the others more 

closely approximate the net contents as given by board-foot rules, 



COMPARISON OF SCALED CUBIC CONTENTS 



37 



TABLE II 

Comparison of Per Cents of Cubic Contents of Cylinders Scaled by Various 
Log Rules, for Logs 18 Inches in Diameter at Small End, with 2-inch 
Total Taper 

Cylindrical contents measured inside bark 



Log rule 



Basis of measure-i Per cent of scale! Per cent deducted 



ment of cylin- 
der, in applica- 
tion of rule 



at 
small 

end. 

Per 
cent 



at 
middle. 

Per 
cent 



if measured at 
other point 



at 
middle 



at 

small 

end 



from contents of 
cylinder to ob- 
tain contents 
given in rule — 
For rules applied 



at 
small 
end 



at 
middle 



Cuhic Standards 
Market or Glens Falls standard 

22-inch standard 

Blodgett or New Hampshire. . . 

Cubic foot — Maine 

Cubic meter — Philippines: 

Short logs 

Long logs 



100 
100 



Cubic Log Rules for Squared 
Timbers 

Quarter girth or Hoppus 

Inscribe;! square 

Two-thirds 

Cube rule, or Big Sandy 



Log Rules Expressed in Board 

Feet but Based on Cubic 

Contents 

Constantine 100 

Tatarian 84.0 

Saco River 72 . 4 

Derby 72 . 1 

Square of Three- Fourths'. ! 71 . 7 

Partridge j 68.8 

Blodgett, converted, ratio 100; 

tolOOOft. B.M ! 




63.4 



56.6 



100 
100 



100 



78.5 



56.5 



59.7 



89.7 
89.7 



89.7 



56 


9 

8 


50 


89 


7 


75 


4 


65 





64 


7 


64 


3 


61 


8 





111.4 
111.4 



111.4 



87.5 



62.9 



66.5 







11.4^ 
11.4^ 


11.4^ 



12.5 
36.6 
37.1 
43.4 





16.0 
27.6 
27.9 
28.3 
31.2 



33.5 



10. 
10. 





10. 




21.5 
43.1 
43.4 
49.2 



10.3 
24.6 
35.0 
35.3 
35.7 
38.2 

40.3 



* Added. 



38 



LOG RULES BASED ON CUBIC CONTENTS 



TABLE 11— Continued 





Basis of 


measure- 


Per cent of scale 


Per cent deducted 




ment of cylin- 


if measured at 


from contents of 




der, in 


applica- 


other point 


cylinder to ob- 




tion of rule 






tain contents 












given 


in rule — 












For rules applied 


Log rule 
















at 


at 


at 


at 


at 


at 




small 


middle. 


middle 


small 


small 


middle 




end. 






end 


end 






Per 


Per 












cent 


cent* 










Log Rules. — Continued 














22-inch standard, converted, 














ratio 1 to 250 ft. B.M 


65.6 




58.9 




34.4 


41.1 


Market, or 19-inch standard. 














converted, ratio 1 to 200 ft. 














B.M 


65.1 




58 . 4 




34 9 


41.6 


Vermont 


63.4 
63.2 




56.9 
56.7 




36.6 
36.8 


43 1 


Vade Mecum (Stillwell's) 


43.3 


Square of Two-thirds 




56.5 




62.9 


37.1 


43.5 


Ake 


62.4 


52.2 


56.0 


58.2 


37.6 
41.8 


44 


French's (Los Angeles) 


47.8 


Calcasieu 


57.8 




51.9 




42.2 


48 1 


Blodgett, converted, ratio 115 




to 1000 ft. B.M 




51.9 




57.8 


42.2 


48.1 


Blodgett, converted, ratio 106 














to 100 ft. B.M 


56.2 




50.4 




43.8 


49.6 


Cuban One-Fifth 




50.1 


45.7 


55.9 


44.1 
49.1 


49 9 


Orange River 


50.9 


54.3 


Maine cubic rule, converted 














185 cu. ft. per 1000 ft. B.M. . 




45.0 




50.1 


49.9 


55.0 


Cumberland River 


45.2 




40.6 




54.8 


59.4 


Delaware or Eastern Shore . . . 


42.4 




38.1 




57.6 


61.9 



Of the cubic log rules expressed in board feet, the Constantine is frankly a cubic 
rule, converted from the cubic foot, but based on the small end of log. The rest 
are suitable neither for cubic contents nor for board feet, since they do not express 
the former nor do they measure the latter correctly (Chapter \). 

These rules are all convertible into cubic units or from one to the other, when 

based on cylinders measured at the same point. 

7rD2 
The formula. Board feet = (l — C) L, can be used to obtain the values for any 

48 

of these rules, by substituting for C the per cent given in the last two columns of 
Table II, e.g. 



RELATION BETWEEN CUBIC MEASURE 39 

To derive the Inscribed Square rule, the cubic contents of cylinders from Table II 
are multiplied by 1 —36.6, or 63.4 per cent. 

To convert the Inscribed Square rule into terms of the Cumberland River rule; 

since 1 —54.8 = 45.2 per cent, the volumes of the two rules are as 45.2 to 63.4. The 

45.2 

Cumberland River rule gives of the Inscribed Square rule, or 71.3 per cent. 

^ 63.4 ^ 

But the Hoppus Rule cannot be converted into terms of either of the above rules, 

since it is measured at the middle point, unless a log of a given diameter and average 

taper is assumed. 

39. Relation between Cubic Measure and True Board-foot Log 
Rules. The conversion of these log rules from cubic to board feet is 
based on the erroneous assumption that logs of all dimensions when 
sawed into lumber will yield the same ratio of board-foot contents to 
cubic contents. In practice, the larger the log, the greater will be the 
ratio or per cent of its contents which makes lumber and the less the 
per cent wasted. For this reason it is not possible to use the same 
standard for scaling both the cubic- and board-foot contents of logs, 
no matter what converting factor is chosen. 

Cubic rules, converted to board-foot contents by a fixed ratio, tend 
to scale small logs too high and large logs too low, as compared to the 
actual sawed contents. The common mistake of the authors of these 
rules is to assume that once the sawed contents of a log of given diameter 
and length is found, the ratio obtained will apply unchanged to logs of 
all other sizes. These rules have therefore fallen into disrepute in the 
scaling of board feet, because of their inconsistencies for this purpose. 

For products such as pulpwood, which utilizes the entire contents 
of the log, these so-called board-foot rules give consistent results for 
logs of all sizes, but do not possess any advantage over the direct use 
of the cubic standard upon which they are based. On the other hand, 
if log rules are intended for the measurement of the actual output of 
1-inch lumber, they must be based on other principles (§ 54). 

The two quantities of measurement, cubic volume, and squared 
board feet obtainable, are incommensurable unless the diameter and 
also the taper of each log is known. The lump sum of a lot of logs 
measured in cubic volume therefore, cannot be converted into board-foot 
measure except by readjusting each individual value by the diameter 
of each individual log. The use of these hybrid rules should be discon- 
tinued in favor of cubic standards on the one hand, and board-foot log 
rules based on correct principles on the other. 



CHAPTER V 
THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 

40. Necessity for Board-foot Log Rules. In other lines of industry- 
it is not customary to measure raw materials in terms of the quantity of 
finished product contained therein. The volume or weight of the raw 
product is the basis of sale. On this basis logs would be sold for theu- 
cubic contents. 

But the purchaser of raw material must know approximately the 
quantity of finished product he can obtain from it before he can estimate 
its value. If the product is to be lumber, the possible yield of boards 
of certain qualities and grades determines for him the value of the logs. 

If it had been found by experience that all logs regardless of size 
would yield the same per cent of their contents in lumber, if sawed by the 
same methods, the cubic standard might have been universally accepted, 
as it was in the Adirondack region. But when it developed that there 
was no consistent ratio of cubic to board feet the only alternative was 
to measure the product directly as boards. 

That the board-foot log rule was needed is shown by the fact that such 
rules were originated independently in practically every lumbering 
region. The contents of the log in sawed 1-inch boards was placed on 
the scale stick, separately for each inch-class and each standard length. 
These board-foot rules soon became practically the universal standard 
of log measure, and are only recently being superseded where the logs 
are used for other purposes than lumber; they will continue to be a 
generally accepted commercial standard of log measure for the lumber 
industry as a whole, until such time as the original stands of timber of 
the country give way to smaller second-growth and closer utilization 
and probably as long as a large percentage of logs are sawed into linnber. 

41. Relation of Diameter of Log to Per Cent of Utilization in Sawed 
Lumber. The sawed output from logs in board feet shows an increasing 
per cent of utilization with increasing diameter of the logs. This result 
may be expressed by the ratio of board feet produced from each cubic 
foot of total volume. This tendency is illustrated in Table III. 

The per cent of utilization in this table is based on the total cubic 
contents of the log as measured by Huber's formula at middle diameter 
inside bark. But practically all log rules for board feet base the con- 
tents upon the cylinder whose diameter is taken at the small end, in 

40 



RELATION OF DIAMETER OF LOG 



41 



which case the volume of the log lying outside the cylinder is neglected. 
On this basis, the apparent per cent of utilization would be con- 
siderably increased over the figures given in the table.^ 



TABLE III 

Relation of Cubic and Boaed-foot Contents op 16-foot Logs with a Taper 
OF 1 Inch in 8 Feet, Based on Tiemann's Log Rule, j^-inch Saw Kerf. 
(§ 63) 



Diameter 
inside bark at 
middle of log. 

Inches 


Cubic 
contents. 

Cubic feet 


Sawed 
contents, 
Tiemann 

Log Rule. 

Feet B.M. 


Ratio 
feet B.M. to 
1 cubic foot 


Volume 
utiHzed 

Per cent 


3 


0.79 


1 


1.27 


10.5 


4 


1.40 


4 


2 . 85 


23.8 


5 


2.18 


9 


4 13 


34.4 


6 


3.14 


15 


4.77 


39.5 


7 


4.28 


23 


5.37 


44.8 


8 


5.59 


32 


5.71 


47.7 


9 


7.07 


43 


6.08 


50.7 


10 


8.73 


55 


6.30 


52.5 


11 


10.56 


69 


6.53 


54.4 


12 


12.57 


84 


6.68 


55.7 


13 


14.75 


101 


6.85 


57.0 


14 


17.10 


119 


6.96 


57.9 


15 


19.63 


139 


7.08 


59.0 


16 


22.34 


160 


7.16 


59.7 


17 


25.22 


183 


7.26 


60.5 


18 


28.27 


207 


7.32 


61.0 


19 


31 . 50 


233 


7.39 


61.6 


25 


54.54 


419 


7.68 


64.0 


31 


83.86 


659 


7.86 


65.5 


37 


119.47 


954 


7.99 


66.5 


43 


161 . 36 


1301 


8.06 


67.2 


49 


209 . 52 


1703 


8.13 


67.7 


55 


263.98 


2159 


8.18 


68.2 


61 


324.96 


2669 


8,22 


68.5 



1 For a 16-foot log 12 inches at middle, with 2-inch taper, and scaling diameter 
at end of 11 inches, the cubic contents are 10.56 cubic feet, the ratio of board feet 
to cubic feet is 7.95, and the apparent per cent of utilization is 665 per cent as against 
an actual 55.7 per cent when the entire volume including taper is taken as the basis. 
For logs with considerable taper, which permits more lumber to be cut from the slabs 
lying outside the cylinder, the apparent per cent of utilization would be still greater, 
while the actual per cent utilized would in reality be lower for such rapidly tapering 
logs than for more cylindrical forms. 



42 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 

It is practically impossible to secure closer utilization than 70 per 
cent of actual total cubic contents of logs in the form of sawed inch 
lumber exclusive of the utilization of slabs, edgings and sawdust when 
circular saws whose kerf is j inch or more are used. By using band 
saws which cut a |-inch kerf and by producing a large per cent of timbers 
and boards thicker than 1 inch, thus reducing the waste from saw kerf, 
the utilization may rise as high as 80 per cent for the larger logs. 

42. Errors in Use of Cubic Rules for Board Feet. By comparing the 
per cent of possible utilization in Table III (§ 41) with the per cents 
given for cubic log rules in Table II (§ 38) the character and relative 
accuracy of these log rules can be judged. For the Blodgett Rule, with 
a ratio of 115 units to 1000 board feet measured at middle diameter, 
the ratio or per cent scaled is 51.9 for all classes and sizes of logs. By 
comparison with Tiemann's Rule this* rule is shown to be correct for 
logs between 9 and 10 inches in diameter, but over-scales smaller logs, 
and under-scales larger logs. The original Blodgett ratio of 100 : 1000 
gives a per cent of 59.7. This is correct for 16-inch logs, too high for 
all logs of smaller diameter and too low for larger logs. 

When the point of measurement is shifted to the small end of log, the 
diameter measurement is correspondingly reduced. When the scale of 
board-foot contents thus determined is compared with this smaller 
cylinder, the per cent of utilization can be expressed for such log rules 
and applies uniformly to logs of all sizes, but only to the small cylinder 
thus measured (§ 81). 

A comparison of the Blodgett Rule applied at the small end of log, 
with the Tiemann rule applied at the middle of log, is shown below. The 
per cents will apply to logs of all lengths whose total taper is but 2 inches. 



TABLE IV 
Comparison of Blodgett and Tiemann Log Rules for Certain Logs 



Diam- 


Total 
taper. 


Per cent of 


Per cent of 


Per cent of 


Per cent of 


Error 


eter 


small cylinder 


total log 


total log 


total log 


in 


log. 


scaled by 


in small 


scaled by 


scaled by 


Blodgett 


Inches 


Inches 


Blodgett Rule 


cylinder 


Blodgett Rule 


Tiemann Rule 


Rule 


6 


2 


56.2 


73.4 . 


41.2 


44.8 


- 2.6 


12 


2 


56.2 


85.2 


47.9 


57.0 


- 9.1 


18 


2 


56.2 


89.7 


50.4 


61.6 


-11.2 


24 


2 


56.2 


92.2 


51.8 


64.0 


-12.2 


30 


2 


56.2 


93.7 


52.6 


65.5 


-12.9 



Cubic rules, as a class, when converted to read in terms of board feet, 
thus tend to over-scale small logs and under-scale large logs, whether 



SCALING LENGTH OF LOGS FOR BOARD-FOOT CONTENTS 43 

they are applied at the middle point, or at the small end. Of the two 
methods the small end gives the most consistent results in board measure, 
since both the actual per cent utilized and the per cent of total con- 
tents scaled decrease with diameter of log. But the decrease in scaled 
contents is always at a lesser rate than that of actual sawed contents, 
hence the tendency to over-scale small logs remains though the size of 
the error is reduced. 

43. Taper as a Factor in Limiting the Scaling Length of Logs for 
Board-foot Contents. Since board-foot contents of logs is equal to 
cubic contents minus waste in sawing, the character and amount of .this 
waste determines the net scale of the log. This waste consists of saw- 
dust, slabs and edgings. As lumber is commonly manufactured with 
parallel edges, in even widths, the custom of sawing boards whose 
length equals that of the log and rejecting all shorter pieces would cause 
a waste not only of the slabs sawed from the cross section at the small 
end but of the entire taper of the log, which would be discarded as 
edgings and slabs. When board-foot rules were first brought into use 
close utilization of short lengths and of wedge-shaped pieces was not 
practiced, and this total waste actually occurred. Under these con- 
ditions the correct point of diameter measurement was not the middle, 
but the small end of the log. Owing to their early origin, the com- 
mercial board-foot log rules now in use are nearly all based on measure- 
ment at the latter point. 

This waste, as measured in cubic volume, increases rapidly with 
increasing length of log. The shorter the logs cut from a given tree, 
the less will be the apparent waste from taper. Long logs, the scaled 
contents of which are based on cylinders measured at their small end, 
would give an entirely different and much smaller scale than if the same 
logs were cut instead into two or more shorter sections and sawed into 
correspondingly shorter lumber. Instead of scaling one log of a given 
top diameter sometimes extending the entire length of the bole, we would 
then have to scale a series of shorter logs, each of which has a top diam- 
eter larger than the preceding one by the amount of the taper between 
the points measured. The sum of volumes of these short logs would 
always exceed that of the single log measured at small end. These long 
logs are usually cut into two or more sections at the mill. For these 
reasons, logs, if their length exceeds a definite maximum are scaled 
as the sum of two or more shorter logs, by taking caliper measurements 
at arbitrary points of division; e.g., a 26-foot log scaled as two pieces 
would be measured at its small end, and at a point 12 feet from the end, 
thus scaling as a 12-foot and a 14-foot log. The scaling diameter of the 
larger or butt section exceeds that of the top end by the amount of the 
taper between the points measured. Each section is thus scaled as a 



44 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 



cylinder, and measured at its upper or small diameter, and the sum of 
volumes of these cylinders gives the scale of the long log. 

The shorter these scaling lengths are made, the larger the total scale 
of the log, but the maximum scaling length must not be shorter than the 
average length of the lumber sawed. In log rules, figures for lengths 
up to 40 feet may be given, and scaling practice often corresponds, but 
in selling logs the U. S. Forest Service limits the scaling length to 16 
feet, which is a standard commonly accepted by timber owners. 

44. The Introduction of Taper into Log Rules. With the increase 
in utilization, much of the lumber formerly wasted in slabs is now secured 
as .short lengths. All log rules in commercial use ignore this product 
and treat the logs as if cylindrical, up to the maximum scaling length. 
To overcome this drawback and include the products from slabs or taper 
without requiring the measurement of logs in separate very short sec- 
tions, the International log rule was constructed,^ based on the principle 




Taper, 2 inches in 16 feet. Vertical scale exaggerated. 

Fig. 5. — Short versus long sections in measuring log contents and in constructing 

a log rule. 

of building up the scaled volume of a log from shorter cylindrical sec- 
tions. These short cylinders are 4 feet long and each successive cylinder 
is increased by |-inch in diameter. The scaled contents of each short 
section is determined, and the sum of these sections gives the scale of 
the log as given in the log rule. The soundness of this method depends 
upon demonstrating that the average taper of most logs is not less 
than that used in the rule, namely, 2 inches in 16 feet. This holds good 
for most Northern and Western species, but for Southern pines the taper 
does not always equal this figure. To guard against excessive error 
from tapers differing from the rate used in the rule, the maximum 
scaling length is limited to 20 feet. 

If the log in Fig. 5 is regarded as a 64-foot log, scaled in four 16-foot lengths by 
any commercial log rule, the scaling diameters are taken at A, B, C and D. The 
gain in scale is caused by inclusion of the shaded portions. 

1 The Measurement of Saw Logs, Judson F. Clark, Forestry Quarterly, Vol. IV, 
1906, p. 79. 



THE INTRODUCTION OF TAPER INTO LOG RULES 



45 



Regarded as a 64-foot log scaled by middle diameter the scaUng diameter is C, 
and the log content is that of a cylinder 64 feet long and of size indicated by C C . 

Regarded as a 64-foot log scaled by end diameter, the scahng diameter is A 
and the log content is that of a cylinder 64 feet long and of size indicated hy A A'. 

Regarded as a 16-foot log scaled at small end, and not in middle, the loss in 
scale is indicated by the shaded portions. This loss is common to all commercial 
log scales based on small end of log. 

But if the contents of the 16-foot log as given in the scale when measured at A 
is built up by measuring the log as four 4-foot cylinders whose scaling diameters 
are A, B, C and D, this loss from taper common to all the commercial log rules, 
except when apphed at middle diameter, is avoided and practically full scale secured. 

A comparison of the results of these three methods of treating taper is brought 
out in Table V. 

TABLE V 
Effect of Different Methods of Scaling a Log 



Length 
of 
log. 


Diameter 
inside bark. 


Scaling 

diameter 

rounded off. 


Scaled as 

one log based 

on small 

diameter. 


Scaled as 

16-foot logs 

each regarded 

as a cy Under. 


Scaled as 
16-foot logs 

allowing 
^-inch taper 
every 4 feet. 


Feet 


Inches 


Inches 


Board feet 


Board feet 


Board feet 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 





24.5 










16 


20.6 


21.0 


328 


328 


355 


32 


19.6 


20.0 


590 


623 


675 


48 


17.3 


17.0 


618 


829 


900 


64 


14.0 


14.0 


531 


962 


1050 



The final column in each of the above examples is the contents of a log 4 feet 
long as scaled by the International log rule. The difference in scale by the other 
methods is due entirely to the length of section scaled as one piece. In column 4, 
this cyhnder, with top diameter indicated, extends the full length of the log. In 
column 5, a new diameter measurement is made every 16 feet, but the cylinder of 
this diameter is 16 feet long. In column 6, the diameter is taken at 16-foot intervals, 
but the cylinder from which this 16-foot log is scaled is built up from four cylinders 
each 4 feet long, and each |-inch greater in diameter than the one preceding it. 

If the average taper of logs is 5-inch for 4 feet, and pieces 4 feet long are mer- 
chantable, then the scale in column 6 is correct. Based on this conclusion the loss 
in scale through neglect of taper is as follows : 



Length of 


Scaled as one 


Scaled as 16-foot 


log. 


log. 


logs. 


Feet 


Per cent loss 


Per cent loss 


16 


8 


8 


32 


13 


8 


48 


31 


8 


64 


51 


8 



Thus the loss in scale is proportional to the length and total taper of the log. 



46 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 

45. Middle Diameter as a Basis for Board-foot Contents. In some 
regions no attempt is made to divide long logs in scaling. While short 
logs are scaled at the end, logs over a given length are measured once at 
the middle and the scale applied to the entire log. In cypress this 
measurement is sometimes taken at a point distant from the small end 
by one-third of the total length. This practice of substituting middle 
for end diameters on long logs and scaling the log as one long cylinder 
whose diameter is thus obtained assumes that the loss in sawing the 
smaller top section will be offset by gain from taper in the butt portion. 
The total scale by this method exceeds that obtained by scaling the log 
as the sum of separate cylinders. 

In theory this measurement of logs for board-foot contents at the middle diameter 
should possess the same advantage over measurement at the small end as for cubic 
contents. But for the former purpose, the factor of waste exercises a definite influ- 
ence on the method of scaling adopted, where for cubic contents it does not. 

With very close utilization of short lengths, it may be assumed that the sawed 
output of two logs of the same middle diameter, one of which tapers rapidly, the 
other gradually, would be nearly equal, since what is lost at the small end of the 
rapidly tapering log would be saved at the larger end. That this is approximately 
true is the premise on which Tiemann based his board-foot log rule ( § 63) on middle 
diameter. 

If, on the other hand, the minimum length of board corresponds with the ordinary 
length of log sawed, the log with rapid taper loses a far greater percent than that 
with small taper, and two logs whose diameters at their small end are the same 
would give equal sawed contents regardless of differences in taper. Since the latter 
condition held when the log rules in common use were invented, this fact, and not 
the difficulty of scaling logs at the middle point, explains the general adoption of 
the custom of basing the contents upon the diameter at the small end. 

46. Definition and Basis of Over-run. The purpose of all log rules 
is to furnish a standard of measurement for logs, fair alike to buyer and 
seller. For board-foot log rules this is best accomplished when the 
rule measures accurately the amount of lumber that may be sawed from 
straight, sound logs. It was the intention and the claim that each of the 
fifty or more log rules extant should perform this service under the con- 
ditions for which it was made; yet in spite of this fact, the contents of 
sound logs of the same dimensions, as measured by different rules, may 
differ more than 100 per cent. 

While some rules based on incorrect premises never were accurate, most of the 
rules as checked by actual mill tests were probably satisfactory when first employed. 
But these rules were not changed to keep pace with the closer utilization brought 
about by the improvements in machinery, methods and markets. Although obso- 
lete as a measure of actual product, they have been retained through custom. It is 
difficult to supplant or alter a commonly accepted standard of measure, even if 
grossly inconsistent and inaccurate. 

Antiquated log rules thus cease to perform the true function for which they 



INFLUENCES AFFECTING OVER-RUN 47 

were intended, of measuring in the log the possible output of lumber. The sawed 
product tends to over-run the scale of contents shown by the log rule. 

An excess of sawed over scaled contents of logs is termed the over-run. 
The over-run is always stated as a per cent of the log scale. The log 
rule, whether accurate or defective, is accepted as the fixed standard, 
giving the same contents for all straight and sound logs of the same 
dimensions. Over-run, on the contrary, will vary with several factors. 
A knowledge of the average per cent of over-run which may be expected 
over the scale enables both buyer and seller of logs to gage their value 
more accurately. As value is dependent on the price of lumber, the 
dealer in logs must know whether for every 1000 board feet of lumber 
scaled by the log rule, there will be obtained say 1250 board feet of 
sawed lumber,' or only the 1000 board feet scaled, for in the former 
case the logs are worth 25 per cent more per 1000 board feet of scaled 
contents than in the latter. 

47. Influences Affecting Over-run. The Log Rule Itself. Two log 
rules giving different scaled contents for logs of the same sizes will yield 
correspondingly different per cents of over-run. Each rule is arbitrarily 
assumed to represent a standard of 100 per cent, the over-run being 
computed in terms of the rule employed. 

For instance, a given quantity of logs when scaled by the Doyle rule may measure 
67,000, and saw out 100,000 board feet. Instead of stating that the log scale gives 
67 per cent of the actual product, with an "over-run" of 33 per cent, the scale is 
taken as the standard or 100 per cent, and the correct over-run in this case is 49 per 
cent. When scaled by the Scribner rule, these same logs may give 85,000 board 
feet. In this case the over-run will be 17.6 per cent since 15,000 board feet is 
17.6 per cent of 85,000 board feet scaled in the log. 

Since the quantity of sound lumber contained in logs can be measured with 
only approximate accuracy, due to hidden defects and other factors, the buyer 
demands a certain margin of safety. A reasonable over-run of from 5 to 10 per 
cent is usually expected. With a properly constructed log rule, the over-run should 
be about the same for large as for small logs. The worst defect which a log rule 
can possess is inconsistency in scale between logs of different sizes (§39). Slight 
irregularities in scale of individual diameter classes may average out in the general 
run of logs. But when the per cent of board-foot contents scaled by a log rule 
increases or decreases in proportion to size of log, there is no way of adjusting it. 
The over-run will then vary with the average size of the logs scaled. Such a rule 
can never give permanent satisfaction to both the buyer and the seller of logs. 

48. Influences Affecting Over-run. Methods of Manufacture. 

With a fixed standard set by a log rule, the greater the economy of man- 
ufacture, the greater will be the over-run. Any factor which reduces 
the waste in manufacture increases the output. The waste in straight, 
sound logs consists of slabs, edgings, trimmings and sawdust. In addi- 
tion, there may be a loss or gain in the scale of lumber due to fractional 
thicknesses not measured in board feet (§ 20). 



48 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 

Saw Kerf. The fewer the number of saw cuts required, the less the 
waste. Lumber sawed and measured to standard thicknesses greater 
than 1 inch therefore increases the total output in board feet. A dimin- 
ished thickness of the saw has a similar influence. Log rules, correct 
when adapted to a j-inch saw kerf, give an over-run of more than 10 
per cent when a |-inch saw kerf i's cut. The use of circular saws cutting 
a j^-inch kerf partially accounts for the small scaled contents given 
by some of the old log rules. 

Slabs. Waste in slabs is reduced by sawing narrow and thin boards 
and short lengths. The short lengths serve to fully utilize the taper in 
long logs, increasing the over-run on this class of material. The method 
of sawing a log also affects the per ceril of utilization of slabs. Slash 
sawing, or sawing alive, as practiced for round-edged boards (§ 21) 
would result in waste where the boards are to be used in their full length, 
and trimmed to square parallel edges. By this method, short boards 
would be secured from but two sides of the log. The usual custom in 
manufacturing lumber of standard lengths is to turn and square the log, 
slabbing all four sides. 

The gain in sawed product, by sawing around, in comparison with slash sawing, 
for square-edged boards, was shown to equal the following per cents, as determined 
by H. D. Tiemann. 

TABLE VI 

Gain in Output Securei) by Sawing Around, Compared with Slash Sawing, 
IN Per Cent of Latter Output 



Diameter 
of log. 


Length 10 feet. 


Length 20 feet. 


Inches 


Per cent saved 


Per cent saved 


6 


15 


22 


7 


14 


18 


8 


13 


15 


9 


12 


13 


10 


11 


11 


11 


9 


10 


12 


G 


7 


13 

: 


4 


6 



Above 13 inches the difference is less perceptible. Where round-edged boards 
are fully utilized and not reduced to square parallel edges, not only does sawing 
around give place to slash sawing, but the per cent of utilization is much greater 
than by either method of sawing for square-edged lumber, due to the shorter lengths 
utilized in working up the round-edged lumber in the factory. 



STANDARDIZATION OF VARIABLES IN LOG RULE 49 

Full and Scant Thicknesses of Boards. Boards not cut to exact 
dimensions, if cut full lose the excess when measured, and if too scant 
are either rejected, or reduced in grade. If cut scant but within pre- 
scribed limits, they are scaled by superficial measure, and increase the 
over-run (§ 20). 

In either case the sawyer to secure full scale of lumber must pro- 
duce boards measuring within j^-inch of the required thickness. This 
is impossible without good machinery. In local custom mills, much 
lumber is manufactured in uneven thicknesses causing a loss in scale 
and reducing the over-run. 

49. Standardization of Variables in Construction of a Log Rule. 
The over-run in sawing logs will depend for a given log rule upon thick- 
ness of saw kerf, average dimensions of lumber, closeness of utilization 
of slabs and of taper, and the exactness of manufactured dimensions. 
All four of these factors are variables. 

For a given mill, the saw kerf alone is constant and even then the waste will vary 
if two or more saws of different kerfs are used. The other factors are variable. 
For different mills, one or more conditions are certain to differ radically, giving a 
corresponding increase or decrease in over-run. Standardization of output and 
methods, possible in mills of the same class serving the same markets, may secure a 
similar degree of slab utilization and of efficiency in sawing to exact dimensions, 
but this still leaves the fourth variable, differences in thickness of lumber sawed, to 
affect the over-run. 

Where the sawed output is in thicknesses less than 1 inch, and expressed in 
superficial feet, the product is not comparable with l-inch lumber and must be 
reduced to terms of 1-inch boards for a true comparison with the log scale. 

Arbitrary Standards. The essentials of any standard of measure 
are fixed qualities and common acceptance. Even a poor or faulty 
standard which is universally used would be better than a number of 
different rules, or a rule which may be changed to suit conditions or 
the preference of the user. These four variables must therefore be 
arbitrarily fixed in adopting values for a standard or common log rule, 
and in the case of most rules which have found wide use this was done. 
The thickness of lumber was fixed at 1 inch, permitting an over-run 
whenever thicker dimensions are sawed. The width of saw kerf adopted 
by the rule was that used at the time and place of constructing the 
rule, and was usually j-inch or larger. Local custom determined the 
width of the narrowest 1-inch board sawed and this fixed the amount 
of waste allowed for slabbing and edging. Taper was disregarded. 
Boards were usually measured only to the nearest full inch of width 
and fractional inches disregarded. SkUl in manufacture was considered 
by checking the results of the rule with the actual sawed output, by 
means of mill tallies. 



50 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 

Variable Sta^idards. As contrasted with these fixed standard rules, 
comes the suggestion ^ for a log rule in which average thickness of lumber, 
saw kerf and degree of utilization of slabs and taper shall be represented 
by variable quantities, and adjusted by each mill owner to suit the 
conditions of manufacture prevailing at the time or for the past few 
months. Such a rule, when adjusted, would eliminate over-run as 
long as the variables in manufacture on which it was computed remained 
unchanged. But as a standard of measurement it could never have 
any general or legal status unless its values were fixed, when it would 
at once be open to the same objections which by its flexibility it sought 
to avoid. 

50. The Need for More Accurate Log Rules. The great question 
with log rules is whether conditions have changed so permanently that 
new rules adjusted to these factors should replace those now in use. 
The j-inch circular saw is still retained in small custom mills, and there 
is a tendency, in regions that have been cut over by big operators, to 
revert to these primitive methods. The operator of a band saw mill 
is probably entitled to the over-run resulting from the use of thinner 
saws and closer utilization. A log rule made to scale closely the out- 
put of such up-to-date plants would exceed the product of the small 
mill. Provided the rule is consistent, a conservative log rule which 
will give an over-run varying in per cent with closeness of utilization 
is probably better for commercial uses than one which aims at securing 
the maximum product from modern mills. 

Log rules based on correct mathematical principles are the only 
rules from which consistent and satisfactory results can be expected, 
and this is a far more important factor than the elimination of over- 
run. If, in addition, such log rules conform to the present conditions 
of manufacture, they have a use in scientific measurements of logs and 
standing timber, as a basis for estimates of volume and growth expressed 
in the board-foot unit. This use of such a rule would justify its exist- 
ence, entirely aside from the question of its possible universal adoption 
as a legal standard of log measure. 

51. The Waste from Slabs and Edgings. The total waste in sawing 
straight sound logs is the sum of the two factors, sawdust, and slabs 
plus edgings. For lumber of a given thickness, such as 1-inch boards, 
the portion of the cross section of the log wasted in slabs and edgings 
may be shown graphically by plotting on diagrams, allowing the proper 
space between each board for saw kerf. From these diagrams it is 
possible to compute the area of this waste, in square inches, and the 
thickness of a ring or collar which will have the same area and thus 
represent the waste from slabbing and edging. 

1 H. E. McKenzie, Bui. 5, California State Board of Forestry, 1915. 



THE WASTE FROM CROOK OR SWEEP 



51 



When this is done for logs of all sizes it is found that except for the 
smaller logs the width of these collars is practically the same regardless 
of diameter. This law does not hold for small logs, because the width 
of the minimum boards remains the same for all logs and as the diameter 
of the log approaches this minimum width of board, the proportional 
waste in slabs and edgings rapidly increases until utilization becomes 
zero and waste 100 per cent for a diameter of log just too small to saw 
out the smallest board or piece that is merchantable. 

The waste in slabbing and edging varies, for any log, with the aver- 
age thickness of the lumber sawed. Logs sawed entirely into 2j-inch 
plank would show considerably 
greater waste in edging than where 
1-inch boards are sawed (§ 21). 
The results shown by diagram are 
confirmed by tests in the mill. 

From these investigations it is 
evident that the waste from slabs 
and edgings is proportional, approx- 
imately, to the surface of the log 
inside the bark. The surface of a 
log is equal to the circumference or 
girth, multiplied by the length. As 
circumference equals irD for all 
logs, the waste from slabs and edging p ^ 
is then proportional to the diameter 
of the log multiplied by its length. 

But the volume of the log in- 
creases as the cross sectional area, 
which is proportional to the square of 
the diameter (§ 27). The amount of 
waste in slabs and edgings from a log 
20 inches in diameter is just twice 

that for a 10-inch log, since the diameter and the surface are doubled. 
But the 20-inch log contains four times the volume of the smaller piece, 
and this reduces the per cent of waste from slabs and edgings based on 
the volume of the larger log to one-half that for the 10-inch log. 

52. The Waste from Crook or Sweep. Log rules apply only to 
straight logs. But the standard as to what constitutes straight logs 
requires definition. For all commercial log rules, this standard permits 
of " normal " crook (§ 93). This is best defined as crook averaging 
not over 1| inches in 12 feet, and including no log which crooks more 
than 4 inches in 12 feet. Crook or sweep in long logs is reduced by 
cutting them into two or more short sections before sawing. Where 




Relative waste in slabs and 
edgings from sawing 2j-inch plank 
and 1-inch boards. If 1-inch boards 
are sawed, the waste is reduced by 
the amount of the shaded portion. 
The greater proportion of waste in 
sawing thick boards comes from the 
side cuts, hence the practice is to 
cut 1-inch lumber from the sides. 



52 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 



very short material such as box boards is used, crook does not cause 
abnormal waste in logs. Care in laying off log lengths in the woods 
to secure the maximum length of straight sections by dividing the 
tree at the points of greatest crook reduces this source of waste to small 
proportions. 

Waste from crook is deducted in scaling on the assumption that 
the merchantable portion of the log must cut boards extending its 
whole length. The influence of length of log upon the waste due to 
crook is very pronounced, and where long logs are divided into shorter 
lengths in the mill they should never be discounted for crook except 
to the extent that this crook will affect the sawed contents of the shorter 
pieces. For lumber longer than 12 feet the influence of crook rapidly 
increases. 

The relation of normal crook to taper is shown in Fig. 7 in which the 
line DE is the axis of the cylinder corresponding to a straight log. The 
line AB is parallel to this axis and tangent to the margin at the small 




Fig. 7. — Method of measuring amount of crook in a log, in inches. The line JM 
represents the proper measurement, coinciding with the shaded portion J A or 
waste in the circle representing small end of log. 

end. The line AC is a straight line connecting the margins of both ends 
of the log. Were the log cylindrical, the line HJ under these circum- 
stances would represent the amount of crook. But the taper gives a 
larger cross-section at JL than at AK. Unless crook exceeds the taper 
for half the log, the cross-section JL when projected upon AK would, 
completely cover it, permitting as much lumber to be sawed as if the log 
were straight. In the diagram the crook exceeds this taper and the 
upper shaded portion of the cross section which represents the small 
end must be wasted in slabs, in addition to the normal slabbing of a 
round log. 

But this waste is incorrectly measured by any other method than 
that shown by the line JM, which is the distance to the surface of the 
log from a line parallel to the axis, and tangent to the margin of the small 
end. This distance gives the crook in inches. 

* For a 16-foot log tapering 2 inches, a crook of 1 to 1^ inches at the 
middle point has no appreciable effect on the output. 



THE WASTE FROM SAW KERF 



53 



By slabbing in the direction of KN this waste may be still further 
reduced, since the cylinder sawed is not parallel with the axis but follows 
the crook at the small end, and takes maximum advantage of taper at 
butt. Logs so crooked that their sawed contents is materially reduced 
are not scaled " straight and sound " or full. Deductions for crook are 
discussed in § 93. The waste from normal crook is included with that 
for slabbing and edging and is in proportion to surface, and hence to 
diameter. 

53. The Waste from Saw Kerf. The total waste in sawdust, unlike 
that in slabs and edgings, takes approximately the same per cent of the 
cubic volume of all logs, regardless of their size. If a log is sawed by the 
method called slash sawing, in parallel saw cuts without squaring it, 
then, after the first slab is removed, there will be one saw kerf to each 




41 



w 



Fig. 8. — Waste incurred as slabs and sawdust in sawing round, straight logs. 

board. The initial saw kerf, and the sawdust wasted in edging, and in 
ripping wide boards into narrower boards, forms an additional percentage 
of waste not exactly proportional to volume. Disregarding this dis- 
crepancy, the fixed per cent of waste from saw kerf for the log is the same 
as the per cent wasted in sawing one board. If the thickness of board 
plus that of the saw is taken as 100 per cent, this waste, for a 1-inch 
board with j-inch saw kerf is as j to 1^ or 20 per cent, while for a |-inch 
saw kerf the proportion is | to 1| or 11.1 per cent. A general formula 
applicable to saws of all thicknesses is as follows: 



Let 1^= width of saw kerf; 
T = thickness of lumber. 



Then 



7"+^ = total volume of board plus kerf, 



54 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 
K 



T-\-K 

T 
T-\-K 



= per cent deduction for saw kerf, 
= per cent of log utilized as lumber. 



Efforts to account for the exact per cent of waste in sawdust have been made, 
by including, first the saw kerf required for ripping or edging one edge, as shown 
in Fig. 8,' and second, the additional saw kerf for the first slab. But neither method 
is complete, since boards are edged when necessary on both edges. The best method 
is probably to include this extra saw kerf, together with the edgings, in the waste 
due to slabbing, leaving the sawdust as a straight per cent of volume. 

Shrinkage. Where shrinkage is considered, or where lumber must be 
sawed a trifle full, the extra thickness which is not measured in the 
green lumber constitutes a waste exactly similar to saw kerf, and can be 
added to the latter factor in the formula before calculating the per 
cent of reduction. 

For instance, if a log rule is intended to measure the output of 1-inch 
lumber after seasoning, and the average shrinkage on inch boards is 
Y6-inch, and saw kerf |-inch, the per cent of waste in small logs is 

¥+i - -^^^^ = 15.8 per cent. 



1+1 + 1^ 1-1875 

^ By the inclusion of one edge, the formula for sawdust would be: 

Volume of unit (W+K){T+K), 

Saw kerf K{W+T+K), 

K{W+T-\-K) 
Per cent of waste ^^_^^^^y,_^-. 

H. E. McKenzie, Bui. 5, California State Board of Forestry, Sacramento, Cal., 
1915. 

By inclusion of the extra saw kerf but not of the cut for edging. 

Number of cuts = N, 

Average saw kerf per board = if -|-t;, 

K 

Volume of unit = T+K + -, 

K 



Per cent of waste 



K' 
T+K+- 



C. M. Hilton, Bangor, Me., 1920. 



TOTAL PER CENT OF WASTE IN LOG 55 

Corrections for Saw Kerfs of Different Widths. Since the per cent of 
waste caused by saw kerf applies directly to the residual volume of logs 
after subtracting the waste for slabbing and edging, the effect of using 
a saw of greater or lesser width than that used in constructing the rule 
can be found in terms of a per cent of the values of the log rule. This 
flat correction can then be applied if desired, to correct timber estimates, 
convert the log rule into one which eliminates over-run from saw kerf, 
or correct the scale of logs to coincide more closely with sawed output. 

For instance, the above rule would utilize 1— .158 or 84.2 per cent of the net 
cubic contents of the cylinder. A saw cutting a j-ineh kerf, with the same allowance 
for shrinkage, calls for the formula, 

i+T& -3125 

= 23.8 per cent, 



l + i+^ 1.3125 

giving 72.6 per cent utilized. The values expressed by the log rule made for the 

1-inch kerf must now be taken as 100 per cent to which the correction will apply. 

76.2 
Then gives 90.5 per cent. The second rule requires values equaling 90.5 per 

84 . 2 

cent of the first, or a straight reduction of 9.5 per cent. 

That this conversion can be accurately made was demonstrated on diagrams by 
H. D. Tiemann, who found that the possible error was less than one-half of one 
per cent.i 

54. Total Per Cent of Waste in a Log. The total per cent of waste in 
a log is the sum of the waste from slabbing and edging, or surface waste, 
and from saw kerf. The proportion of this total waste represented 
respectively by slabbing and by sawdust will depend upon which of 
these deductions is made first, and whether the sawdust made in slabbing 
and edging is included as part of the waste in slabs and edgings, or is 
counted as part of the waste in sawdust. If the deduction for sawdust 
is made first, it will include a fixed per cent of the cubic volume of the 
log. If on the other hand, the slab waste is first deducted as a ring or 
collar of a given thickness, the subsequent deduction for saw kerf, 
although the per cent is the same, applies only to the residual volume of 
the log. 

The total per cent of waste, and its distribution between these two factors is 
illustrated in table VII. Let slab waste equal a ring f-inch in thickness or a 
reduction of 1.5 inches in diameter. Sawdust, for j-inch kerf, equals 20 per cent. 
The per cent of waste will vary with diameter of logs, as shown : 

In column 2 the per cent of waste is seen to be approximately one-half as great 
for 20-inch logs as for 10-inch logs. 

1 Proc. Soc. of Am. Foresters, Vol. V, 1909, p. 29. 



56 THE MEASUREMENT OF LOGS— BOARD-FOOT CONTENTS 



TABLE VII 

Distribution of Waste between Slabbing and Sawdust 



1 


2 


3 


4 


5 


6 


7 


8 


Diameter 

at 

small 

end of 

log. 

Inches 


Waste in 
slabbing. 

Per cent 


Waste in 

sawdust 

20 per cent 

of 

remainder 

of log. 

Per cent 


Total 

waste 
Columns 

2+3. 

Per cent 


Waste 

saw kerf 

in 

slabs. 

Per cent 


Total 

waste 
saw kerf, 
Columns 

3+5. 

Per cent 


Waste in 

slabs less 

saw kerf 

in 

slabs. 

Per cent 


Utiliza- 
tion.* 

Per cent 


10 
20 
40 


27.75 
14.44 

7.27 


14.45 
17.11 
18.54 


42.20 
31.55 
25.81 


5.55 
2.89 
1.45 


20 
20 
20 


22.20 
11.55 

5.82 


57.80 
68.45 
74.19 



* Of the small cylinder not including taper. 

The waste in slabbing would be exactly proportional to diameter except for the 
fact that the volume of the hollow cylinders representing the collar deducted for 
slabs is not directly proportional to the outer surface of the respective cylinders in 
logs of different sizes. The same relation is seen to hold whether or not the slab 
waste is deducted before or after the sawdust. (Columns 2 and 7.) 

Since the per cent of slab waste is roughly proportional to D, while that from 
sawdust is as £)-, the sum of these two factors causes the total per cent of waste to 
decrease as shown in column 4, instead of remaining constant as in column 6. The 
rate of decrease is less rapid than in columns 2 or 7 since only a portion of the waste 
decreases in per cent with increasing diameter of log. 

Were the total waste in logs proportional to D^ as is the waste from 
saw kerf, log rules could be converted from cubic to board feet by a 
single ratio. But since the part of this waste due to slabbing is pro- 
portional to D, the per cent of total waste decreases with increasing diameter 
by a rate which is the sum of these two factors and is therefore directly 
proportional to neither D nor D^. This explains the increasing per cent 
of utilization secured in sawing larger logs and the need for log rules 
based directly upon the board-foot unit and not derived by conversion 
of cubic units. 

To derive an accurate log rule, not only must the waste from slabs 
and edgings be deducted separately from the waste from saw kerf, but 
the correct amount must be deducted for each source of waste. A rule 
which deducts too much for slabs and too little for saw kerf will deduct 



TOTAL PER CENT OF WASTE IN LOG 57 

too much on small logs, where the slab waste is normally high, and too 
little on large logs, where the greater portion of the deduction is for saw 
kerf. Such a rule can be correct only for a single diameter class where 
the two errors happen to balance. 

On the other hand, if too small a deduction is made for slabs, and 
too large for sawdust, small logs may be overscaled, while the increasing 
per cent of utilization possible in larger logs will not be shown in the 
scale (Column 8), and the rule therefore tends to under-scale large sizes. 



CHAPTER VI 

THE CONSTRUCTION OF LOG RULES FOR BOARD-FOOT 

CONTENTS 

55. Methods Used in Constructing Log Rules for Board Feet. The 

great variation in the contents of different log rules for board feet, and 
the variation in accuracy and consistency of these rules is due to the 
methods used in their construction as well as to the factor of over-run 
resulting from closer utilization. 

Four general methods have been used in constructing such rules. 
These are: 

1. By mathematical formulae. A formula is used, which derives the 
board-foot contents of the log directly from its diameter and length, by 
allowing for reductions from D"XL for cubic volume, waste in saw 
kerf, waste in slabs, and reduction of residual volume to board feet. If 
the principles used in making these reductions (§ 54) are correct and the 
amounts used are also correct, such log rules are superior to diagram 
rules, but if errors in either principles or amounts of deduction are 
introduced into the formula, the rule is worse than useless. 

2. By diagrams. Full-sized circles of all diameters are drawn on 
large sheets of paper, representing the top ends of the logs. On these 
cross sections of the log the ends or cross sections of the boards which 
could be sawed from these logs are drawn, leaving between each board a 
space equal to the width of the saw kerf. The area of boards in square 
inches is then reduced to board feet by the factor -^ X length in feet, for 
logs of a standard length, and from this, for logs of all lengths. 

3. By tallying the actual sawed contents of logs at the mill for differ- 
ent diameters and lengths. Owing to the variables introduced by the 
thickness of lumber sawed, and by taper, this method has seldom been 
accepted as the sole basis for a log rule, but has been extensively used 
to check the accuracy of rules made by the preceding two methods. 

4. By conversion of the cubic contents of logs into board feet, after 
deducting a fixed per cent of this total cubic contents for waste in saw- 
ing and slabbing. As shown in Chapter V, all board-foot log rules 
constructed on this basis are fundamentally wrong. 

A fifth method has been used, which is a combination of methods 
1 and 2 or 3, namely, to alter or correct the values of an existing log rule, 
by means of mill tallies obtained in sawing. The author of such cor- 

58 



THE CONSTRUCTION OF LOG RULES 59 

rections may give a new name to such a rule, or may state that it is 
an old rule corrected. Such corrected rules while undoubtedly better 
than the originals have so far failed of adoption in place of the rules 
from which they were made, owing to the force of custom in perpetuating 
established standards even if in error. 

56. The Construction of Rules Based on Mathematical Formulae. 
Many efforts have been made to evolve a formula which will give an 
accurate basis for a board-foot log rule. Of these the erroneous formulae, 
or rules of thumb, based on a fixed conversion factor are most common. 
Of those which recognize the fundamental difference between waste from 
slabs, and waste from saw kerf, we have two groups, distinguished 
not by principle, but by the method of procedure dependent on whether 
the deduction for saw kerf is made first, from the total contents of the 
log, or whether that for slabs and edgings is first deducted, and the 
waste from saw kerf then taken from the residual volume. 

Method of Deducting Slabs First. When the first plan is used, a constant, a, 
representing in inches the double width or thickness of the hollow cylinder or sur- 
face layer wasted in slabs, edgings and crook, is first deducted from the diameter of 
the log at small end. From the area of the smaller circle thus obtained, the required 
per cent is subtracted for saw kerf, shrinkage or surplus thickness of board required 
in sawing. 

The residual area of the circle in square inches is converted into board feet for 
logs 1 foot long, by dividing by the factor 12. Disregarding the taper, the volume 
of a log of any length is found by multiplying the contents by length in feet. 

D = diameter of log in inches; 
a = inches subtracted from diameter, a constant ; 
D—o = reduced diameter of log after subtracting waste from slabs and edgings; 

= reduced area of small end of log in square inches; 

4 

b—per cent of volume deducted for saw kerf; 
1 — 6=per cent remaining after deduction for saw kerf; 

L = length of log in feet ; 
B.M. = volume of log in board feet; 



then 



7r(D-a)2 L 
B.M. = (l-i,)-4-A - 

48 



Illustration 



Let a = 1 .5 inches, representing a collar of .75 inch thickness deducted for 

slabs, etc. 

b = 20 per cent representing a j-inch saw kerf. 



60 THE CONSTRUCTION OF LOG RULES 

Then for any log, 



B.M. = (l-.20)^— — ^L. 
4o 



For a 12-inch log IG feet long, 



/3. 1416(12- -.„, ,,^ 

B.M. = .80 ^ 16 

\ 48 

= 92 board feet. 



±^y 



Method of Deducting Sawdust First. — By the second method, the per cent of 
waste in saw kerf is first deducted from the entire volume of the log. From the 
residual volume the amount to be further subtracted for slabs, edging and crook is 
taken. This is a smaller per cent than by the first method, as shown in Table VII, 
column 7 since the sawdust used in slabbing is not included, and it is for convenience 
computed in the form of a plank of width and length equal to the log, and whose 
thickness is varied to give the required volume of waste. 

Let A equal the width of this plank in inches. This is taken as a constant. 

Then, 



/ ttD'- \ L 



Illustration 

Let b = 20 per cent — sawdust allowance, 

A = 1.767 inches, the thickness of a plank whose width is equal to D, and 
length to L — for slabbing allowance. 
Then for any log. 



B.M.= 



rD2 

.80( ■ — )-1.767D 



For a 12-inch log 16 feet long, 

B.M. =[.80(. 7854 X 122) -1. 767 Xl2]|f, 
B.M.=92 board feet. 

This result shows that for 12-inch logs, after subtracting 20 per cent from log for 
sawdust, a plank 1.767 inches by 12 inches gives a deduction from the net volume, 
equal to method 1 when a collar .75 inch thick is first deducted and 20 per cent for 
sawdust taken from the remainder. 

The two methods are not absolutely interchangeable. Their relation may be 
shown by algebraical means. 

Substitute C for (1-6). 

Then C = per cent left after subtracting saw kerf. 

Since D is in inches, and L exerts no influence on the relative values, the areas 
of the small end of log, left after subtracting total waste, should be equal, and can 
be expressed in square inches for each formula as: 

CniD-ay CirD^ ^^ 

= AD. 

4 4 

Then, 

C(1.5708aD-.7854a2) 



A=- 



D 



COMPARISON OF LOG RULES BASED ON FORMULA 
The results, for certain diameters are shown below: 



61 



TABLE VIII 

Thickness of Plank to be Deducted for Slab Waste to Coincide with a 
Collar 1.5 Inches Thick. Sawdust Allowance 20 Per Cent 





Double thicknes.sof col 


Corresponding thick- 


Ratio of thickness of 


Diameter of 


kir deducted for slab 


ness of plank to be 


of plank to collar 


log. 


waste previous to de- 


deducted after de- 






ducting .sawdust. 


ducting sawdust. 




Inches 


Inches 


Inches 




3 


1.5 


1.414 


0.940 


6 


15 


1.649 


1.099 


9 


1.5 


1.728 


1.152 


12 


15 


1.767 


1.178 


18 


1.5 


1.800 


1.200 


40 


1.5 


1.849 


1.233 



The use of these ratios would give identical results by both methods. But in 
application the second method usually stipulates that the thickness of plank shall 
be constant for all logs. This results in a greater proportionate deduction for slabs 
on small logs than by the first method. This deduction is more in accordance with 
the actual results of sawing, owing to the increasing effect of minimum widths of 
board on per cent of loss in slabbing (§51). The best application is to adopt a 
ratio which applies to medium-sized logs, and use this for all logs, large and small. 

If a log rule is constructed to deduct the waste which actually occurs in sawing, 
it must be based on one or the other of these two formulae. If the waste allowances 
are correct for the conditions assumed, there will still be over-run when other condi- 
tions apply, but the per cent of over-run will be practically the same for all sizes, 
the rule is consistent, and the results are subject to correction by a fixed ratio or 
per cent. 

If the waste allowance for either slabbing or sawing, or both, are incorrect for 
the conditions assumed, the rule will not only give over- or under-run, but will also 
be inconsistent, the per cent will differ with diameter, and the rule will not be subject 
to correction by a fixed ratio, and will lack the basic requirements of a standard of 
measure. 

57. Comparison of Log Rules Based on Formulae. In constructing 
a formula log rule, the correct application of tlie deduction for saw kerf 
presents no great difficulty. In the International rule, an extra deduc- 
tion of Ye-inch was made for shrinkage. Other rules neglect all factors 
but the actual width of saw kerf (§ 53). 

The deduction for slabs, edging and normal crook requires determination not 
only from diagrams but from practical tests. The following amoimts are deducted 
by the log rules given below, expressed both as a "collar" deduction from diameter, 
(a), and as a thickness of plank {A), to correspond with the two methods described 
(§ 56). 



62 



THE CONSTRUCTION OF LOG RULES 



TABLE IX 

Deductions for Slabbing and for Saw Iverf, for 12-inch Logs, in Ten Log 
Rules Based on Formul.«. The Basis Used in the Rule is Shown in 
Heavy Type. 



Log Rule. 



Deduction 

from diameter 

for 

slabbing. 

Inches 



Equivalent 

deduction in 

form of a 

plank 

thickness. 

Inches 



Saw kerf 

plus 
shrinkage. 

Inches 



Deduction 

for 
saw kerf. 

Per cent 



International 

Universal 

Preston : Large logs 

Small logs 

British Columbia. . 

Click 

Clement 

Wilson 

Thomas 

Baughman * 

Champlain 

Doyle 

Baxter 



1.73 
1.66 
1 75 
1 50 
1.50 
1 25 
1.18 
1.00 
1.00 
0.87 
0.83 
4 00 
1.00 



12 
00 

04 



8 P 16 



1.77 



77 
42 
32 
17 
17 
05 
00 
GO 
GO 



15.8 
20.0 
20.0 
20.0 
27.3 
23.6 
25.0 
22.2 
22.0 
20.0 
20.0 
4.5 
33.8 



* Diagram rule. 

Of the rules above cited, the British Columbia and Doyle are the only ones used 
extensively at present. The table is instructive as an indication of the proper allow- 
ances to make for slabbing. The test of a formula is actual comparison with sawed 
output. The deductions in the International rule were determined by careful 
measurement on logs actually sawed. The Champlain rule is known to be too 
close a rule, with too small an allowance for slabs. The British Columbia rule 
neglects shrinkage and is a good standard. The Click rule was carefully checked 
by sawed output. These results indicate that for 1-inch lumber sawed to exact 
dimensions, an allowance for slabbing of 1 .5 to 1 .75 inches subtracted from diameter, 
or one-half this deduction as the single thickness of the collar, is a fair allowance 
for slabbing. This allowance would be too small for lumber of greater average 
thickness than 1 inch or for very small logs. 

When the deduction is made in the form of a plank whose width equals the 
diameter, D, of the log, the thickness of plank required to make it equivalent to the 
collar deduction is from 1.75 to 2 inches for 12-inch logs, slightly more for larger 
logs, and decreasing in thickness for smaller logs. But where the deduction is made 
in this form, as in the International and Champlain rules, it is used as a constant 
for all dimensions (§ 59 and § 62) with results corresponding more closely to actual 
waste than by the first method. 

The allowance for saw kerf, on all log rules in commercial use, is j-inch or over. 
The International rule in its original form gives values for a |-inch saw kerf, which, 
with the other allowances, gives a rule intended to measure the output of modern 
band mills. 



McKENZIE LOG RULE, 1915 63 

58. McKenzie Log Rule, 1915. This log rule is a universal formula 
and not a commercial standard or true log rule. It is intended to 
reduce all the variable factors in the production of sawed lumber to 
elements in a formula, which will permit the determination of a local 
rule that will accurately measure the sawed output in the log for any 
condition, and eliminate over-run. 

The factor of taper is treated by building up the log in 8-foot sections, 
permitting the use of whatever actual average taper coincides with that 
of the logs sawed. The allowance for slabs, edging and crook is made by 
the first method, that of deduction from the diameter previous to sub- 
tracting saw kerf. Shrinkage could be included with saw kerf, if neces- 
sary, but the author does not mention it. 

The formula is the one already shown to be correct and universal for board-foot 
log rules, 

L 

B.M. = (l-fe).7854(I>-a)2— . 

The saw kerf allowance, h, is computed to include width as well as thickness of 
lumber sawed (§ 53). To this general formula the author adds a constant, c, to 
offset excessive taper on small logs. 

The principal utility of this log rule will be found in determining, in advance of 
sawing, the amount of over-run which may be obtained from logs scaled by a com- 
mercial rule, or to test the results in over-run to be expected by the use of different 
log rules and different methods of manufacture. The objections to adopting it as a 
standard of measure are stated in § 49. 

Reference 
Bui. 5, California State Board of Forestry, by H. E. McKenzie. 

59. International Log Rule for |-inch Kerf, Judson F. Clark, 1900. 

In constructing this rule, modern conditions of manufacture in large 
mills were presupposed. The values of the rule as published are for a 
band saw cutting a |-inch kerf and are rounded off to 5 and 10 board 
feet, thus approaching the principle of a decimal rule. Saw kerf is 
first subtracted, allowing j^-inch for shrinkage, or a total of -j^ inch. 
The deduction for slabs and edging, including a normal crook of from 
1 to \\ inches is then made in the form of a plank measuring 2.12D. 

The forrpula reads: 

B.M. = (.66D2-2.12D)— . 
12 

The rule was constructed as follows: Since the per cent of waste in saw kerf plus 
K ^ 

shrinkage is — this becomes for inch boards or 3 parts in 19, which gives 

1+A 16-1-3 ' ^ 

.158, and the factor for residual volume is .842. Then, 

.842(.7854Z)2) = .66Z)2. 



64 THE CONSTRUCTION OF LOG RULES 

The deduction 2.12D was determined from tests of sawed logs, including all crook 
of 4 inches or less. 

Since the log is divided into 4-foot lengths, the sum of which gives the scale, 
the formula reads for each length, 

B.M. = (.66D2-2.12D)y*2 
= .22D^-.71D. 

A taper of ^-inch in 4 feet is allowed. D is thus increased by ^-inch for each succes- 
sive section and the sum of the scale of the separate 4-foot cylinders gives the scale 
of the log (§ 43). On account of the allowance for shrinkage the rule is based in 
reality on the production of Irg-i^ch boards measured as inch boards. A minimum 
width of 3 inches, and a minimum length of 2 feet are adopted as standard, no piece 
to contain less than 2 board feet. Standard values were published, it being the inten- 
tion of the author to furnish a commercial log rule that could be accepted as a com- 
mon standard for the measurement of logs as sawed in modern mills using a band 
saw cutting a j-inch kerf. 

60. International Log Rule for ^-inch Kerf, Judson F. Clark, 1917. 

For general adoption as a standard commercial log rule, the |-inch rule 
is open to the objection that it over-scales the product of most small 
mills, since it is seldom that such mills use saws cutting less than j-inch 
kerf, or make close use of the taper of the log. A log rule which gives 
a safe margin, and which permits mills using thin band saws and up-to- 
date equipment to secure an over-run of about 10 per cent is more 
acceptable as a commercial standard than one which scales for the 
closest possible standard of utilization. For this reason, Mr. Clark 
has computed values for the International rule, for j-inch saw kerf. 
This form of the rule is here published for the first time from values 
furnished by its author (Appendix C, Table LXXX). To obtain this 
rule, the original values for the |-inch rule were reduced by 9.5 per cent 
and then rounded off to the nearest 5 or 10 board feet. The rule is 
recommended as a standard for scientific measurements of volume and 
growth in terms of board feet, for regions where the product is manufac- 
tured ])y small mills using circular saws cutting a j-inch kerf. 

61. British Columbia Log Rule, 1902. This is the only case of the 
legal adoption and application in commercial scaling of a new log rule 
based on sound scientific principles, as the direct result of a thorough 
investigation. In 1902 a commission of three men prepared from dia- 
grams a rule to suceed the Doyle Rule for the province, which was 
adopted in 1909 as the Statute rule. 

Their results were embodied in a formula reading: 

"For logs up to 40 feet in length deduct H inches from the diameter of the small 
end inside the bark; square the result and multiply by the decimal .7854; from 



OTHER FORMULA RULES . 65 

the product deduct three-elevenths; multiply the remainder by the length of the 
log and divide by twelve." Or, 

B.M. = (1 -fV).7854(Z)-1.5)2- 



12 



= .727^ -—. 

4 12 



The minimum width of board used was 3 inches. 

For logs over 40 feet in length, an increase in diameter is allowed on half the 
length of the log amounting to 1 inch on the diameter at the small end, for each 
10 feet in length over 40 feet. Thus for logs from 41 to 50 feet long the contents 
of the butt cylinder is scaled by a diameter 1 inch larger than the top end; for logs 
from 51 to 60 feet long, the rise allowed is 2 inches, etc. 

This allowance for taper is absurdly small and constitutes the only weak point 
in the rule. It is a concession to the low standards of utilization practiced in the 
province at the time. 

62. Other Formula Rules, Approximately Accurate, Both in Princi- 
ples and Quantities. When a log rule is constructed by using the prin- 
ciples embodied in the standard formula, and when in addition, the 
amount of deduction for both saw kerf and slabbing is approximately 
correct, the resultant log rule will be far more accurate and consistent 
than any of the commercial rules in common use except the last men- 
tioned. Several rules have been constfucted, whose values differ only 
because of slightly different allowances for waste, as shown in Table IX. 
Seven such rules are given below. This completes the list of log rules 
known to the author, and based on diameter at small end of log, which 
deserve to be classed as fundamentally correct standards for board-foot 
contents of saw logs. 

Champlain Log Rule, A. L. Daniels, 1902. This log rule, intended as a perfect 
rule for 1-inch boards, is based on j-inch saw kerf and neglects taper. It is for 
perfect logs. The deduction for slabs and edging, without normal crook, is made 
equal to a 1-inch plank or ID. No shrinkage is considered. The diameter is taken 
at small end. Were it not for an over-run secured from taper or the methods of 
sawing used, logs would never saw out what this rule calls for. The quantities 
given are above normal in cylindrical contents for short logs. This error is offset 
by neglect of taper, so that in long logs the rule falls below the International. 

This rule has not been used commercially, except in a few instances in Vermont. 
The formula is : 

L 

B.M. = (.62832D-D)^— . 
12 

The author of the Champlain log rule realized that the slab allowance was too 
small for actual conditions. By increasing the width of plank deducted for slabbing 
to 2D, a modification, termed the Universal log rule was computed, using the formula, 

L 
B. M. = (.62832D2-2Z))— . 
12 



66 THE CONSTRUCTION OF LOG RULES 

This rule compares favorably with other theoretically accurate rules except that 
it shares the common fault of neglecting taper. Mr. Daniels states (1917), that he 
favors the use of the Champ lain rule as the more accurate of the two . 
Wilson Log Rule, 1825. 

B.M. = .807-^ — . 

4 12 

By Clark Wilson, Swanzey, N. H. Originated in 1825, and computed for j-inch 
boards. Now obsolete. This was unquestionably the first formula rule. The author 
was a mathematician, and "estimated the difference in yield in gain of the large 
logs over the small ones, and then calculated the intermediate spaces by nearly 
regular integral differences as logs increase in size. The author intended it for 
|-inch boards. It is recorded that E. A. Parks later used it for 1-inch boards, which 
use resulted in a lawsuit." (John Humphrey, Keene, N. H.) 
Preston Log Rule, An Old Rule. 

Large logs, B.M. = .80^ 



Small logs: B.M. = .80 



1 12 

w{D-1.5yL_ 
1 12' 



Still used in Florida. Known locally as a seller's rule. Sold in Jacksonville, Fla., 
by H. & W. B. Drew Co. 

Thomas' Accurate Log Rule. 

■K(D-\yL 
B.M. = .78- — 



12 

For j-inch saw kerf. Also computed for |-inch kerf. 

Click's. Log Rule, 1909. 

7r(D-1.25)2L 

B.M. = .764-^ . 

4 12 

By A. C. Click, Elkin, N. C, 1909. This rule was based on 1-inch boards averaging 
6 inches in width and makes reduction for saw kerf of j-inch as per the formula 
(§ 58), used by McKenzie. Other rules for different widths of saw kerf were worked 
out by the author. (Forestry Quarterly, Vol. VII, 1909, p. 145.) 

Carey Rule, Date Unknown. This was a caliper rule to be applied to middle 
diameter, and was used for round edge boards^-inch thick. The values given are 
almost identical with the Wilson ruie. Former^ used in Massachusetts. 

Clement's Log Rule, 1904. 

12 



B.M.: 



.75 -1.18D 

\ 4 ; J 



This log rule illustrates the use of a rule of thumb, based on correct mathematics. 
The above formula is expressed thus: Multiply half the diameter by half the circum- 
ference, then subtract half the circumference. The remainder will be the total 
amount of feet board measure, in a 16-foot log. 
This becomes : 

B.M. = (.7854D2-1.57D)— , 
16 

from which the above formula is derived. 

With the exception of the Preston, none of these rules is in commercial use. 



TIEMANN LOG RULE 1910 67 

63. Tiemann Log Rule, H. D. Tiemann, 1910. All of the com- 
mercial log rules in use are open to the criticism that the taper is dis- 
regarded, thus causing the over-run to vary according to the length 
and amount of total taper of the log. The International rule, in which 
taper is included, is not in commercial use to any extent. But one 
attempt has been made to take proper cognizance of taper by the method 
of applying a log rule for board feet to the middle diameter instead of the 
small end. Most rules employing this method are cubic-foot rules or 
based on cubic contents. The Tiemann log rule on the other hand is 
a true board-foot rule based on a j^-inch saw kerf. The rule was made 
from actual mill tallies accurately adjusted for saw kerf and for exact 
thicknesses and the results worked out graphically by curves. Quite 
remarkably the curves were found to correspond very closely to the 
exceedingly simple formula 

B.M. = (.751)2 -2D)^, 



which equals (.IIQ^^-Ldo) 



7rD2 . _\L_ 
12' 



The application of the rule is limited by its author to lengths not 
exceeding 24 feet. 

This log rule applies to logs scaled in the middle. When this is 
possible, the rule is more accurate than any other board foot log rule, 
since neither the variation in taper nor length of log affects it. It can 
be adjusted to apply to the small end just as well as any other rule can, 
but it is intended primarily for middle diameter as this largely elimi- 
nates errors in estimates of taper. For scientific records it is of distinct 
value. It is superior to the International rule as it eliminates taper 
as a variable instead of averaging it. The obstacles to converting this 
rule or any other rule into equivalent values at small end are discussed 
in § 31. The rule is given in Appendix C, Table LXXXIV. 

64. Formula Rules Inaccurately Constructed. Baxter Rule. If 
the allowance for slabbing in a formula rule is excessive, and that for 
sawdust too small, the resultant volumes will be too small for logs of 
small diameters and too large for large logs, thus giving not only an 
inaccurate but an inconsistent rule. If these errors in deducting waste 
are reversed, slabbing allowance being too small, and that for sawdust 
too large, the reverse is true, and the large logs will be under-scaled. 

Baxter Log Rule. In adopting a rule of thumb for the construction of a log rule, 
the author may have in mind a certain result, but the rule when expressed in a formula 
may give quite a different result. 

The Baxter Log Rule was constructed by the rule "Subtract 1 from the diameter 
inside bark at the small end, square the remainder, and multiply by .52. The result 



68 THE CONSTRUCTION OF LOG RULES 

is the contents of a 12-foot log" (hence — gives the contents of any log). This squar- 
ing and subsequent subtraction of one-half the square was intended to give suffi- 
cient deduction for both slabs and saw kerf. But it actually gives, 

7r(D-l)L 

B.M. = .662- '—. 

4 12 

The factor 1, for ^4, is insufficient for slabs and the factor .338 for C is far too great 
for sawdu.st, corresponding in fact to a kerf of -i.inch. The rule therefore greatly 
underscales large logs. Its inconsistency makes it worthless. 

65. Doyle Log Rule. Synonyms: Connecticut River, St. Croix, 
Thurber, Vannoy, Moore-Beeman (in part), Ontario, Scribner (erro- 
neously) . 

This rule is used almost to the exclusion of all other rules for hard- 
woods in parts of the Ohio Valley, and for Southern yellow pine. Its 
use is extensive in every eastern state outside of New England and 
Minnesota. In the West, it is not used to any extent. 

The Doyle rule reverses the error of the Baxter rule by deducting 
too large a per cent for slabbing and not enough for sawdust. The wide 
use of this rule has caused losses of millions of dollars to owners selling 
logs and standing timber, by improper and defective measurement of 
contents. The prevalence of its use is due first to the simplicity 
of its application as a rule of thumb. The rule reads: Deduct 4 inches 
from the diameter of the log as an allowance for slab. Square one- 
quarter of the remainder and multiply the result by the length of the log 
in feet. The result is the contents in board feet. Timber cruisers 
estimate logs in 16-foot lengths. For this length of log the rule would 
read: Deduct 4 inches from the diameter of the log inside bark, and 
square the remainder. The result is the contents of the log in board 
feet, by the Doyle rule. A rule as easily applied as this was sure to be 
popular. 

The second reason for its wide use was its substitution for the old 
Scribner rule in Scribner's Log and Lumber Book, after this publication 
had already attained a large circulation. As this book was widely 
accepted as a standard and almost the only publication on log rules, 
the impetus given to the use of this inaccurate rule by this substitution 
was tremendous. 

The third reason for the continued use of the Doyle rule is the same 
which operates to prevent reform in the use of log rules in general. 
Custom, or habit of using it, is fixed. So far has this gone that the 
States of Arkansas, Florida and Mississippi prescribe its use by statute. 
Added to this is the fact that a rule favoring the buyer will be advocated 
by this class to its own advantage. 



DOYLE LOG RULE 



69 



The seller can defend himself against the use of a short measure if 
the latter is consistent and its per cent of error is known. But with a 
log rule like the Doyle, the per cent of error differs with every scale of 
logs or stand of timber and it is practically impossible to determine the 
actual loss without remeasuring the logs by a correct log rule or tally- 
ing the sawed contents. 

Since it will be impossible to displace this log rule by better standards unless 
its vicious character is fully understood, the exact nature of the error should be made 
clear. The original form of this rule read "Deduct 4 inches from the diameter 
for slabs, then squaring the remainder, subtract one-fourth for saw kerf and the 
balance will be the contents of a log 12 feet long." The sawdust allowance as 
intended, would have corresponded to a i^-inch saw kerf. The author evidently 
figured that 4 inches of slab would square the log sufficiently so that the sawdust 



rT 





Fig. 9. — Actual deductions for slabs and for saw kerf made by the formula of the 
Doyle rule, for logs 6 inches, and 28 inches in diameter respectively. 

The square ABCD is the supposed residue after deduction for slabs, while the 
outer inscribed circle represents the actual residue. The inner inscribed circle 
represents the residual percentage shown as board feet by the rule. The sawdust 
allowance is, therefore, the difference between the outer and inner inscribed circles, 
whose area is but 4.5 per cent of the contents of the cylinder. 



allowance could be applied in this manner to the squared or partially squared stick. 
His fundamental error lay in his method of deducting for slabbing and edging. As 
shown, the waste from slabs and edging does not amount to a reduction of 4 inches 
in the diameter, but to about 1.75 inches, and instead of being slabbed from four 
sides, it is distributed evenly over the entire surface as a collar. The assumption 
made resulted in an actual deduction for slab far in excess of what was intended, 
this excess in turn reducing the sawdust allowance from an assumed 25 per cent to 
negligible proportions. 

The above diagrams (Fig. 9) will explain the reason for this inconsistency. 

The diagram for the larger log shows that the squaring of the timber would not 



The standard formula -(D— 4)^ gives the volume 
4 



require a 4-inch slab allowance 

.7854(D— 4)- as the actual net result of deducting 4 inches from the diameter of the 



70 THE CONSTRUCTION OF LOG RULES 

log. This was the point overlooked in constructing the rule. The deduction so 
made is in its eiTect "a deduction for slabbing and edging although not so intended. 

That it was not intended is shown by the instructions for next deducting one- 
fourth of (/)— 4)^ "for saw kerf." But this leaves .75(D— 4)- for all logs, instead 
of .7854(D— 4)2, which is a further reduction of but .0354(0—4)^, the actual reduc- 

.0354 
tion for saw kerf = . 045 or 4 .5 per cent of the cylindrical contents for saw kerf 

instead of the 20 per cent of the same cylinder required by a j-inch saw kerf. The 
remaining 21.5 per cent of the supposed saw kerf is a true slab deduction of 4 inches 
from diameter. Thus the amounts and proportions of slab deductions are grossly 
out of balance and this ruins the rule. 

This early form was not known as the Doyle rule. The present form, first 
published in the decade 1870-80 was advertised as a new rule. The scale is identical 
with the older form but the change in the wording of the rule to its present form 
still further concealed the flaw in its construction. 

The formula for the Doyle rule is: 

/D-4^ 
B.M.= — 
\ ^ 
corresponding to the standard formula: 

B.M. = .955-^ -—. 

4 12 

The true sawdust allowance can be shown by the following comparison: 

'D-4\2 
j L=.0625(D-4)2L. 

The area contents of the cylinder D— 4, 

■K L 

-(D-4)2— = .06547(D-4)2L. 

Since the cylinder D— 4 represents the log minus true slab deduction, = 

•^ '.06547 

95.5 per cent or the log minus both slabs and sawdust. ^ 

66. Effect of Errors in Doyle Rule upon Scaling and Over-run. 

The effect of this overbalancing of the respective allowances is to cause 
this rule to give zero for the contents of logs 5 inches in diameter while 
for logs above 47 inches, the scale yields more than 80 per cent of the 
cubic contents, thus, for ^-inch kerf, eliminating slab waste altogether. 
The over-run would thus vary with increasing diameter, from infinity 
to zero. 

When the Doyle rule Is applied to long logs, with a small top or scaling diameter, 
the over-run becomes proportionally greater. A careful test, under direction of 
the courts in Texas where logs of given sizes were actually sawed (Extending a 
Log Rule, E. A. Braniff, Forestry Quarterly, Vol. VI, 1908, p. 47), showed that 
for 24-foot logs sawed by circular saw,, the Doyle rule gave an over-run for different 
diameters, as shown in Table X. 

^ The author is indebted to material published by H. E. McKenzie in Bui. 5, 
CaUfornia State Board of Forestry, for this discussion of the error in the Doyle rule. 



EFFECT OF ERRORS IN DOYLE RULE 



71 



TABLE X 
Over-run, Doyle Rule. Texas 



Diameter at 
small end. 


Sawed product. 


Scale 
Doyle Rule 


Per cent of 
over-run 


Inches 


Board feet 






&- 6f 


35 


6 


483 


7- 7f 


49 


14 


250 


8- 8i 


61 


24 


150 


9- 91 


76 


37 


105 


lO-lOf 


95 


54 


76 


11-llf 


112 


74 


51 



The over-run steadily diminishes with increasing diameter until at from 36 to 40 
inches the rule gives practically full scale for j-inch kerf and normal allowance for 
slab, disregarding taper. 

An investigation made in 1904 for the Province of Ontario by Judson F. Clark, 
showed that the volume of the average log cut in the Province had decreased in 
25 years by 63 per cent and at that time averaged 61 board feet and 12 inches in 
diameter. From mill tests of pine logs sawed with i^-inch kerf, the per cent of 
over-run was as follows, for 12-foot logs: 



TABLE XI 
Over-run, Doyle Rule. Ontario 



Diameter of 

log at small 

end. 


Scale by Doyle rule. 


Actual output of 
inch lumber. 


Per cent 

of 
over-run 


Inches 


Board feet 


Board feet 




6 


3 


14 


366 


8 


12 


30 


150 


10 


27 


50 


85 


12 


48 


76 


58 


14 


75 


108 


44 


16 


108 


144 


33 


18 


147 


186 


26 


20 


192 


234 


22 



When the average log ran between 18 and 31 inches, the defects of this rule were 
not so apparent, and the over-run was not excessive. But as the size of the logs 
cut grows less with the advent of second-growth and closer utilization, the rule 
becomes impossible. Its continued use in many regions is due largely to the fact 
that logs are not often bought and sold, but the timber is purchased on the stump 
and the owner is unaware of his losses. This rule must eventually be superseded 
either by a more consistent standard or by the rejection of board-foot measure 



72 THE CONSTRUCTION OF LOG. RULES 

altogether. No owner of small logs or of young standing timber can afford to sell 
on the basis of a scale or estimate made by the Doyle rule. As it stands, this rule 
is a serious obstacle to the profitable marketing of second-growth timber, hence to 
the practice of forestry. 

67. The Construction of Log Rules Based on Diagrams. In con- 
structing log rules based on diagrams (§ 55), tiie quantity of 1-inch 
boards contained within a given diagram may vary, due to four different 
factors. The first is whether a 1-inch board or a saw kerf is placed on 
the center line. For some diameters the one method gives the most 
lumber, for others the alternate plan, depending upon the relation of 
the total diameter to the sum of the diameters of boards plus saw kerf. 
The second factor is the minimum width of the boards to be sawed. The 
narrower the board, the greater will be the product from circles of a 
given diameter. The third source of variation lies in the choice of 
plotting all boards as if slash sawed, or else arbitrarily choosing a given 
method of sawing around or squaring the log on the diagram, with 
boards taken from the slabs. The fourth factor is the acceptance or 
rejection of fractional inches in the boards inscribed in the circle. When 
all boards are read to the nearest full inch in width, dropping all frac- 
tions, some diagrams will lose a much larger per cent than others— while 
in actual sawing, these variations tend to even up. 

For circles of the same diameter and with the same minimum width 
of board and saw kerf, the board-foot contents will evidently vary con- 
siderably according to the treatment of these four factors in construction 
of the diagram. In a well-constructed consistent set of diagrams, the 
values in board feet should increase by a regular progression. This 
can be shown by plotting the original quantities on cross-section paper 
and connecting the consecutive points by straight lines. Irregularities 
are revealed by sharp angles in this continuous line. Most diagram 
log rules show considerable irregularity, which the authors made no 
attempt to smooth out, as could have been done by means of this graphic 
plotting. A wholly inexcusable variation of such rules is caused by 
increasing the average width of slab allowed on large logs. This increase 
does not conform to the actual practice in sawing and results in a larger 
over-run on large logs. It is the principal defect in both the Scribner 
and the Spaulding diagram log rules. The Maine or Holland rule, 
by avoiding this error, secured a more consistent result. 

Diagram log rules tend to give the scale of perfect logs under a given standard 
for saw kerf and width of slab. The waste for normal crook and irregular form 
cannot be shown. Since the commercial rules have ordinarily allowed too thick a 
slab or too wide a minimum board or have rejected fractions, this loss is compen- 
sated, but formula rules if accurate are more practical and convenient. 

Baughman Log Rules. As an example of a diagram rule which is too perfect 
for commercial use, since it neglects shrinkage and normal crook and includes frac- 



SCRIBNER LOG RULE, 1846 73 

tional inches, can be cited the Baughman log rules for j-inch and |-inch saw kerfs 
respectively. The results obtained from these diagrams are so consistent that they 
conform to the tjqjical formula for a perfect log rule. 

B.M. = .si "" ~' — — for i-inch kerf, 
4 12 



and 



7r(D-l)2L 

B.M. = .90 for 1-inch kerf. 

4 12 



In practice the use of these rules would give an under-run: i.e., the logs would not 
saw out the scale. 

In these diagrams the minimum board was 4 inches, the lumber exactly 1 inch. 
The 1-inch board was always placed in middle of diagram. Taper was neglected. 
H. R. A. Baughman, Indianapolis, Ind. 

68. Scribner Log Rule, 1846. Synonym: Old Scribner. The 
Scribner log rule is the oldest diagram rule now in general use. But for 
the unfortunate substitution of the Doyle rule for this rule in Scribner's 
Log and Lumber Book, its use would now be practically universal. 
The rule held its own in the North and West, and is the legal standard 
for Minnesota, Wisconsin, West Virginia, Oregon, Idaho, and Nevada. 
It is the standard prescribed in timber sales on National Forests through- 
out the West and by the Dominion Forestry Branch of Canada. 

The rule was published previous to 1846. The diagrams are for 
1-inch lumber, and \ inch saw kerf. The width of the minimum board 
was not stated but the author modified an earlier edition of his rule by 
increasing the allowance for slab on larger logs. As a result of this 
unfortunate error, the rule gives a larger over-run on logs above 28 inches 
than on smaller logs. The products of the diagrams were evidently 
not evened off. The values, when plotted, show great irregularities, 
but except for the factor just noted, the general tendency of the rule is 
consistent. 

The original values were for logs from 12 to 44 inches in diameter in 
sections 15 feet long, " the fractions of an inch inside the bark not 
taken into the measurement." Taper is not considered on logs of the 
lengths used. These factors the author intended to offset normal crook 
and concealed defects. Values were then given for logs from 10 to 24 
feet in length. 

Modification to a Decimal Rule. Two important changes in this rule 
have been made to meet the demands for a universal log rule. It has 
been changed to a decimal rule, and values for logs below 12 inches, 
and above 44 inches have been added. The practice of modifying a log 
rule in scaling by reducing it to even tens, in order to eliminate the col- 
umn of unit feet in adding, is found in connection with several rules. 
With the Scribner, instead of dropping odd feet, thus reducing the scale, 



74 



THE CONSTRUCTION OF LOG RULES 



the odd feet were rounded off to the nearest ten, values over 5 feet 
being raised, while 5 feet and under are dropped. The average scale 
of even a few logs by this method is practically identical with that 
obtained by the original rule as the errors are compensating. This modi- 
fied rule is known as the Scribner decimal rule. 

Extension below 12 Inches. For values below 12 inches, the original rule pro- 
vided no figures. The lack of a formula permitted individuals to supply their own 
values for these sizes. As early as 1900, the Lufkin Rule Company tabulated the 
decimal values then in use, under three schedules, termed A, B and C, shown below. 

To read in board feet, add a cipher to each figure. 

TABLE XII 
Decimal Values Below 12 inches for Scribner Log Rule 





Decimal A 


Decimal B 


Decimal C 


Length. 


Diameter — inches 


6 7 8 9 


10 


11 


6 7 8 9 10 11 


6 7 


8 9 


10 


11 


Feet 


Board feet, in tens 


12 
14 
16 
18 
20 
22 
24 


112 3 
112 3 
12 3 4 
12 3 4 
12 3 4 

12 3 5 

13 4 5 


4 
4 
5 
5 
6 
7 
7 


5 
6 
6 
7 
8 
9 
10 


12 2 3 4 4 
12 3 3 4 6 
2 3 3 4 5 7 
2 3 4 5 6 8 

2 3 4 6 7 8 

3 4 5 7 8 9 

4 5 6 7 9 10 


1 2 

1 2 

2 3 
2 3 

2 3 

3 4 
3 4 


2 3 

2 3 

3 4 
3 4 

3 4 

4 5 
4 6 


3 
4 
6 

6 
7 
8 
9 


4 
5 
7 
8 
8 
9 
10 



Still other values resulted from the use of the full scale, rather than the decimal 
form. In the Woodsman's Handbook, (1910 Forest Service), values for 16-foot logs 
used by a company in New York (Santa Clara Lumber Co.) were pubhshed. These 
values were adopted by the Canadian Forestry Branch in 1914. The State of Minne- 
sota adopted standard values differing slightly from these figures. Wisconsin 
adopted definite values by law for these sizes, conforming exactly to the Decimal "C" 
scale given above. Idaho prescribes that the Scribner Decimal Scale be used with- 
out specifying values and both "A" and "C" scales are in use in the state. In 
Oregon and West Virginia the "Scribner Scale" is called for by statute, leaving the 
question open for values below 12 inches. 

The weight of custom is at present in favor of the use of the Decimal "C" values 
for this rule, and the utihty of the Scribner Decimal Rule would be improved by a 
universal adoption of this standard. 

Extension above 44- inches. With the adoption of the rule by the Forest Service, 
its use on the Pacific coast required an extension from 44 to 120 inches. In this 



SPAULDING LOG RULE, 1868 75 

instance a similar but worse confusion might have resulted, but was avoided by the 
adoption of a single standard of values prepared by the U. S. Forest Service about 
1905, and published in the Woodsman's Handbook, 1910 edition. The extension 
(made by E. A. Ziegler) was based on a comparison of the curve formed by the 
plotted values of the rule with similar curves for the formula rules such as the 
International, and for the Spaulding rule. Ziegler states, "It might be described 
as an extension built on an old rule by graphic methods checked with the correct 
mathematical formula in which the slab waste varies with D and the kerf with D-, 
and compared with the accepted rules in the Northwest, notably the Spaulding." 
The extension was built up on a r2-foot log, and applied to lengths of from 8 to 
16 feet. As a concession to logging methods in the Northwest, logs up to 32 feet 
were scaled without taper by this rule. 

No such difficulties in extension are encountered with rules constructed by the 
use of correct formulae, since the values of logs of all sizes are in this way determined. 

Attempt to Improve the Rule. Further efforts to modify this log rule have been 
made in order to even off the irregularities of value between contiguous sizes. 
Examples of this are the Hanna log rule, 1885 (John S. Hanna, Lock Haven, Pa.), 
the White rule, 1898 (J. A. White, Augusta, Mont.) and a local rule used by M. E. 
Ballou & Son, Becket, Mass., 1888, adopted from Scribner rule, for small logs. Such 
modifications unquestionably improve the rule, but the minor irregidarities do not 
appreciably modify the scale of a large number of logs of different sizes. The con- 
fusion which would result in attempting to secure universal agreement on any change 
in accepted values for this rule has prevented their adoption, and the values still 
stand as they were originally determined, subject only to the conversion to decimal 
form. 

The Scribner Decimal " C " log rule in spite of its imperfections 
comes the nearest at present to fulfilling the demand for a universal 
commercial log rule, because of its present wide acceptance and use 
(§ 13), and reasonable consistency in over-run. The latter reason alone 
makes it preferable to the Doyle rule. Not even this rule, however, 
does justice to logs below 12 inches in diameter; and in regions of second 
growth and small logs, a closer and more accurate rule is preferable. 

69. Spaulding Log Rule, 1868. Synonym: California Rule. The 
Spaulding Log Rule was adopted by statute in 1878 as the standard for 
California, and the values were given. It was constructed by N. W. 
Spaulding of San Francisco in 1868 from diagrams of logs from 10 to 96 
inches in diameter, using an y|-inch saw kerf, and 1-inch lumber, and 
afterwards tested by sawing logs of each size in two mills. The size of 
the slab (width of minimum board) was varied according to the size of 
the log. This error of construction tends to increase the over-run in 
large logs. The values were given for lengths from 12 to 24 feet. The 
author directed that longer logs be scaled by doubling the values in the 
table, and this practice was incorporated in the statute. Thus the 
rule neglects taper altogether. In scaling, this principle is not applied 
to logs longer than 40 feet. It constitutes the most serious defect of the 
rule at present. Owing to the large saw kerf considerable over-run is 



76 THE CONSTRUCTION OF LOG RULES 

secured by modern band saws but the rule is fairly consistent, as are 
all well-constructed diagram rules. 

70. Maine or Holland Rule, 1856. Synonym: Fabian's. This 
is the most accurate and consistent diagram rule in common use (§ 55). 
It was constructed in 1856 by Chas. T. Holland for 1-inch boards, 
allowing for a j-inch saw kerf and for a minimum width of board of 6 
inches. Fractional parts of a foot amounting to over .5 are reckoned as 
a whole foot, those less than .5 are rejected. This resulted in a more 
consistent rule from the diagrams. The rule is applied at the small 
end of log and disregards taper, so cannot be applied to the scaling of 
long logs without considering them as sections. The best practice now 
limits the length of these sections to 16 feet (§ 43). 

71. Canadian Log Rules. The practice of adopting standard log 
rules by statute has been followed by New Brunswick, Quebec, Ontario 
and British Columbia. Their use is practically universal in the pro- 
vinces. 

The New Brunswick Rule, 1854. This rule is the statute rule of 
the Province and is probably based on diagrams. Values for from 5 to 
10 inches were added by later regulations. Logs 26 feet and over are 
measured in two lengths. The small end is used and the rule is based 
on 1-inch lumber. 

Quebec Log Rule, 1889. To construct this rule, diagrams of logs 
from 6 to 40 inches in diameter were divided into 1-inch boards. A 
second set was divided into 3-inch deals, using |-inch kerf. The mean 
of the two resultant contents was taken, and from this an arbitrary 
deduction was made, ranging from to 17 feet. Taper was neglected. 
This scale is applied at the small end for logs up to 18 feet in length, 
above which the average diameter of the two ends is taken. The rule 
is the statute rule of the Province.^ 

The British Columbia Rule is discussed in § 61. 

72. Hybrid or Combination Log Rules. The inconsistency of the 
Doyle rule by which small logs are under-scaled and large logs over- 
scaled has led to its combination with the Scribner rule. The values 
of the latter rule drop below the Doyle rule at 28 inches. 

Low values in the log rule favor the buyer of logs. In purchasing 
large logs, especially hardwoods, the Doyle rule was considered unsafe. 
The combined rule, termed the Doyle-Scribner, retains the low values of 

* The statute rule of the province of Ontario is the Doyle Rule which was 
adopted in 1879. In spite of the facts brought out in an investigation in 1904, 
that in that one year the Province lost 134 million board feet on the scale, equiv- 
alent to 23 per cent of the contents of the logs cut, by reason of this rule, the 
influences in favor of its retention were too strong to be overcome and it is still 
the standard rule of the Province. 



GENERAL FORMULA FOR ALL LOG RULES 77 

the Doyle rule up to 28 inches, and substitutes the low values of the 
Scribner rule above that point. 

The reverse of this process was adopted by the State of Louisiana 
in 1914. The values of the Scribner rule below 28 inches were combined 
with those of the Doyle rule for 29 inches and over, and the resultant 
hybrid rule, known as the Scribner-Doyle rule is the official rule of the 
state. 

The Doyle and Baxter rules were also combined, using the Doyle 
values up to 19 inches, with those of the Baxter rule for the remaining 
diameters. Both the Doyle-Scribner and the Doyle-Baxter are cut- 
throat rules calculated to give the buyer the maximum advantage of 
the -defects of both rules. The Scribner-Doyle rule has no advantage 
over the straight Scribner rule since most logs are below 28 inches in 
diameter. 

73. General Formulae for All Log Rules. When log rules have not 
been constructed by a formula, but from diagrams or mill tallies, no 
formula can be found which will give the exact values of the rule. But, 
consciously or not, the authors of log rules have attempted to deduct 
the waste from saw kerf and from slabbing and edging and the average 
results which they obtained, or the actual treatment of these two fac- 
tors is revealed by reducing these rules to the nearest approximate 
formula. 

The general form of such a formula is: 

BM. = iaD^-+bD+C)— 

in which aD^ covers the per cent reduction of volume for sawdust after reducing the 
square to a circle, bD gives the reduction of diameter or surface for slabbing and edg- 
ing, while C is a constant added in an effort to correct irregularities in the rule itself. 

L 
The factor — reduces square inches to board feet. 
12 

Cubic rules converted to board feet correspond exactly to the formula, 

B.M. = (aD2)— 
12 

or to 

7rD2 

B.M. = (l-6) L. 

4X12 

Perfect formula rules correspond to the formula, 
BM. = {aD^+bD)— 



or to 



B.M. = (l-&)-^ -L. 

4X12 



78 THE CONSTRUCTION OF LOG RULES 

But imperfect or irregular diagram or formula rules require the formula, 

BM. = {aD^+bD+C)— 

or 

B.M. = ((l-6)-^^^-CML. 
\ 4X12 / 

The first of these sets of formula? was originated by A. L. Daniels, the second by 
H. E. McKenzie. By Daniels' formula, the values of logs of three sizes will give 
the formula. For the following rules, the formula; read: 

Doyle, B.M. = (.75D-'-6D + 12)— , 

Scribner, B.M. = (.555D2- .55D-23)— ; 

12' 

Maine, B.M. = (.635D2-1 .45D+2) — ; 

12' 

Champlain, B.M. = (.62832D2-D)— ; 

L 

Vermont, B . M . = ( . SOD^)— . 
12 

By the McKenzie formula, adding the constant C gives the following for: 
Spaulding, B.M. = ( (1 - .266)-^'^ 2)L; 

Scribner, B.M. = I (1 - .266)^"^^ -3 |L; 
' 4X12 / ' 

Maine, B.M. = ( (1 - .222)-^^ - .67 |L. 

\ 4X12 / 

These formulaj permit of analysis and comparison of different log rules. 

74. The Construction of Log Rules from Mill Tallies. Graded 
Log Rules. A log rule based directly on mill tallies or the measured 
product of sawing logs into lumber will have no over-run provided the 
variable conditions of manufacture coincide with those which determined 
the contents of the logs from which the rule was made. But this is 
never the case. Standard log rules made for 1-inch boards do not con- 
form to mill tally of lumber sawed partly into 2-inch plank, or even if 
sawed full or Ijig-inch in thickness. Standard rules for square-edged 
lumber fall far short of measuring the product of small logs sawed and 
tallied as round-edged boards. The board foot as a cubic measure will 
not indicate the quantity of surface or superficial feet of lumber pro- 
duced in sawing f-inch boards. 

Where it is desired to obtain, in the log, the probable actual contents 
in boards, and existing rules are unsatisfactory, a new rule may be worked 



THE MASSACHUSETTS LOG RULE 79 

out based directly on mill tallies. Unfortunately, most of the rules so 
obtained are not standardized for lumber of a given width, as 1-inch 
boards, but include the mill run, with varying per cents of thicker plank. 
This requires a statement as to the basis of the rule. Even when based 
on arbitrary per cents of 1-inch and thicker lumber such a rule may be 
superior, for local use, to one of the older commercial rules. 

A mill tally, upon which a local log rule can be based, will also serve 
two other purposes if rightly conducted, namely, a check on the amount 
of over-run to be obtained from logs of different sizes if scaled by an 
existing log rule (Doyle rule, § 65), and an analysis of the product of 
the log by grades of lumber, leading to the construction of graded log 
rules. 

For the single purpose of constructing a log rule for sound logs with 
normal crook (§ 52) but two operations are required. Each log is meas- 
ured, preferably at both the small end, inside bark, and the middle 
diameter outside bark, and its length recorded. The contents of each 
board sawed from the log is then tallied, and the total found, from which, 
by averaging for logs of the same dimensions, and the use of graphic 
plotting (§ 138) the log rule may be obtained. 

When mill-scale studies are made to check a given log rule, and to determine 
contents of logs by grades, from which a graded log rule is constructed (§87), the 
work is planned as follows: Each log is given a number, and is scaled as it enters 
the mill. A second man stationed at the edger places this number on the first and 
last board sawed from the log. A lumber grader at the grading table indicates the 
grade of each board, while a fourth man tallies the board-foot contents of the piece 
on a ruled blank which contains columns for each standard grade. As the scaler 
and grader are usually employees of the mill the work requires two extra men in 
the mill. 

The study is usually extended to include defective logs, which are kept separate 
in the final averages, since the original scale of such logs is a matter of judgment 
subject to wide errors. (Appendix A, § 361 .) 

By a proper system of numbering the logs in the woods, a mill scale study may 
be applied to determine the graded contents of entire trees for the construction of 
graded volume tables (§ 165). 

Reference 

A Mill-scale Study of Western Yellow Pine, H. E. McKenzie, Bui. 6, Cali- 
fornia State Board of Forestry, Sacramento, Cal , 1915. 

75. The Massachusetts Log Rule for Round-edged Lumber. This 
log rule is constructed for round-edged and square-edged boards as 
sawed from small logs for close utilization of second-growth timber. 

The per cent of square-edged lumber sawed varies from to 50 per cent, increas- 
ing with diameter of log. The rest of the cut was round-edged. The rule is for 
J-inch saw kerf, varying in the per cent of round- or square-edged boards included. 
It is based on mill taUies of 1200 logs down to 4 inches at small end. The rule is 



80 THE CONSTRUCTION OF LOG RULES 

expressed in two forms, one for application to diameter at small end, inside bark, 
the other to diameter outside bark at middle of log. The latter form would apply 
only to species with bark of similar average thickness to the second-growth white 
pine on which the latter is based. The utility of this rule as a standard is inter- 
fered with by the fact that a certain per cent, not stated, of 1 5-inch and 2|-inch 
lumber was included with 1-inch boards in its construction. The results are there- 
fore somewhat too high for 1-inch lumber. 

This log rule indicates that the contents of logs measuring from 4 to 10 inches 
in diameter at small end are from 20 to 50 per cent greater when scaled by this rule 
than by the International |-inch rule. Above 12 inches, the excess is not over 
10 per cent. Since these boards are measured at their average face, taper is fully 
utiUzed, while waste from slabs and edging is reduced to a minimum. The result- 
ant per cent of utilization is very consistent for logs of all sizes; hence it shows a 
marked gain in the small sizes over the per cents utilized in square-edged boards as 
shown in Table III. 

The importance of a log rule of this character in scaling the board-foot contents 
of second-growth timber in regions utilizing round-edged boards is obvious. Rules 
of this character are nearly as satisfactory as the cubic foot in measuring small timber. 
For complete accuracy in applying this rule to other species, the average taper 
must be known, or the average thickness of bark. Similar local log rules have 
been made for loblolly or old field pine in the Atlantic Coast States. 

76. Conversion of Values of a Standard Rule to Apply to Different 
Widths of Saw Kerf and Thickness of Lumber. Where over-run or 
under-run is caused by a difference in the width of saw kerf used, or in 
the thickness of hunber sawed, from the standards used in the log rule, 
the per cent of this difference between scaled and sawed contents due to 
these factors may be easily determined, and applied, if desired, to the 
scale; or it may be incorporated in a new set of values or local log rule 
similar to those made from mill tallies. 

For saws of different widths. 

Let isr = width of saw kerf in standard rule; 

K' = width of saw kerf used in sawing. 
Then 

1 

-— — - =per cent of lumber, minus saw kerf by standard rule; 
l-\-K J , 

1 



- =per cent of lumber using different saw kerf. 
1+K 

The correction to apply to the standard rule in terms of per cent is: 



Per cent correction = 100 X , 



1+A' 
e.g., the International rule, 3-inch kerf plus j^g-inch shrinkage = ^-inch = . 3 125, 

1 

100 X =76. 3 per cent. 

1.3125 ^ 



CONVERSION OF VALUES OF A STANDARD RULE 



81 



For a i^-inch saw kerf plus re-inch shrinkage = i\- = . 25, 



Then, 



1 

100 X =80 per cent. 

1.25 ^ 



80 

100 X = 104 . 8 = +4 . 8 per cent. 

76.3 



The following table will convert values for the International j-inch log rule to 
products of saw kerfs of other widths, allowing i^-inch shrinkage in each case as 
for the original rule. 

TABLE XIII 

Conversion of International Rule j-inch Saw Iverf for Other 

Widths of Kerf 



Width of saw 

kerf. 

Inches 


Per cent 
utihzed* 


Per cent correc- 
tion to obtain 
product for 
desired kerf 


7 
64 

1 

8 

3 
16 

1 

1 

3 

g 
7 
16 


85.4 
84.3 
80.0 
76.3 
72.7 
69.6 
66.7 


+ 11.9 
+ 10.5 

+ 4.8 


- 4.7 

- 8.8 
-12.6 



* This per cent applies only to the residual portion of the log after deducting the waste for 
slabbing and edging. The ratio between the per cents utilized is the basis for correcting for saw 
kerf. 

Log rules which make no allowance for shrinkage may be adjusted in the same 
manner by omitting this factor. Table XIV, Page 82. 

Correction for lumber thicker than the standard. For this jjurpose the same 
formula as for saw kerf is used, substituting the actual thickness of lumber {t) for 
1 inch, and using X as a constant representing saw kerf. 

Let 1 = standard thickness of lumber; 

<= actual thickness of lumber. 
Then, 

=per cent of lumber, minus saw kerf by standard rule; 

1+K ^ ' J , 

t 



=per cent of lumber, with thickness of t; 

t-^K 



and 



1+K 



=per cent correction. 



t+K 
For j-inch saw kerf the results obtained are given in Table XV, Page 82 (§ 48) : 



82 



THE CONSTRUCTION OF LOG RULES 



TABLE XIV 

Conversion of Log Rules with |-inch Saw Kerf and No Shrinkage 
Allowance to Other Widths of Saw Kerf 



Width of 
saw kerf. 
Inches * 


Per cent 
Utilized 


Per cent correc- 
tion to obtain 
product for de- 
desired saw kerf 


7 
64 

1 
8 

1 
4 

f 


90.2 
88.8 
84.3 
80.0 
76.2 
72.7 
69.6 


-t-12.7 

4-11.1 

+ 5.4 



- 4.8 

- 9 1 
-13.0 



* Rules made by first subtracting slabbing and edging may evidently be altered for different 
widths of saw kerf, as these deductions are directly proportional to volume, and are applied to the 
reduced cylinder only. Where, as with the International rule, the deduction for saw kerf is made 
before subtracting AD for slabs and edging, this rule still holds good, since the per cent of cor- 
rection is not applied to the entire log, but to the values in the rule, which already exclude AD. 
If worked out for the log, independent of the rule, the sawdust in the slabs is deducted before 
the factor AD is found, and for larger saw kerfs this factor AD would be proportionally smaller, 
so that the total net product in lumber is the same as if computed by the above correction. 



TABLE XV 

Per Cent of Increase in Sawed Lumber Caused by Sawing 
Lumber of Different Thicknesses j 





Increase in sawed 


Thickness of himber. 


product over 1 inch 




lumber. 


Inches 


Per cent 


u 


4.1 


H 


7.1 


If 


9.4 


2 


11.1 


21 


12.5 


3 


13.6 



t In preparing tables of volume for Connecticut hardwoods (Bui. 96, Forest Service), Frothing- 
ham used the International rule, reduced for a J-inch saw kerf by subtracting the required 9.5 
per cent of volume from-values for i-inch saw kerf. Complaint was later made that in applying 
these tables to logs sawed in mills using j-inch saw kerf, the output over-ran the tables. This 
was due not to error in the tables, but to the production of a large proportion of thick planks, 
thus reducing the sawdust waste. 

These per cents are applied to the scale of 1-inch lumber. When 50 per cent of 
the output is in 2-inch plank, the correction would be 50 per cent of 11.1 per cent, 



LIMITATIONS TO CONVERSION OF BOARD-FOOT LOG RULES 83 

or 5.55 per cent. As the increase in per cent of correction in the total scale becomes 
less with increasing thickness of boards sawed, this method is more accurate than 
that of computing the average dimensions of the products sawed. In the above 
case the latter would have been I5 inches, calling for a correction of 7.1 per ceftt 
instead of 5.55 per cent. 

Correction for thin lumber based on superficial contents. In a similar way, 
log rules for 1-inch lumber may be corrected to give the product in superficial board 
feet for lumber sawed to thicknesses less than 1 inch. Since the board, of whatever 

thickness, measures 1 superficial foot, the "per cent of utilization" will be ;, ( being 

t-\-K 

thickness of board, K, saw kerf. For ^-inch kerf and 1-inch lumber, the standard 

1 

1 t I K 
per cent is =80 per cent. Then the correction per cent is . 

1+K 



TABLE XVI 

Correction Per Cents for Contents of Logs in Superficial Board Feet 
FOR Lumber Sawed Less than 1 Inch in Thickness 



Thickness 

of 

lumber. 

Inches 


Saw kerf. 
Inches 


Per cent of 
utilization 


Per cent for 
inch lumber 


Correction per 

cent to add to 

log rule for 

1-inch boards 

Per cent 


s 

8 
f 

i 


1 


133.3 
114.3 
100.0 

88.8 


80 
80 
80 
80 


66.6 
42.9 
25.0 
11.1 



77. Limitations to Conversion of Board-foot Log Rules. It is thus 
seen that a correction of the total scale of logs regardless of diameter or 
length can be made whenever thid correction takes the form of a straight 
per cent of the volume of the scale. In addition to the effect of saw kerf 
and thickness of boards, this principle applies to cubic rules erroneously- 
used for board feet (§ 38). But no true board-foot log rule can be con- 
verted by a constant or flat per cent into the values of any other log 
rule, unless the deduction for waste from slabs and edgings is identical 
for both rules, and the difference is wholly due to the use of different per 
cents of waste for saw kerf. Otherwise, the conversion factor will vary 
with diameter of log. Since tables of tree volumes and the scale of a 
number of logs include logs of different sizes, such volume tables or 
scale totals must be remeasured in the log in order to determine the 
values for any other than the log rule originally used. 



84 



THE CONSTRUCTION OF LOG RULES 



78. Choice of a Board-foot Log Rule for a Universal Standard. As 
long as opinions and customs differ with regard to tlie measurement of 
taper, scaling length, saw-kerf allowance and amount of waste in slabbing 
which should be expressed in log rules, it will be impossible to reach 
an agreement on a common standard. Meanwhile, custom is working 
towards the elimination of rules which have not found favor and all but 
about ten log rules in the United States can already be classed as obsolete. 

A log rule becomes obsolete when it ceases to be used, regardless of 
the reasons for its disuse. Poor rules should, and sometimes do, become 
obsolete because they do not give satisfaction. But good and con- 
sistent rules may also become obsolete or may never be taken up, because 
the use of other and inferior rules is so firmly intrenched that a substitu- 
tion is impractical. Rules which scale so closely as to permit no over- 
run will be very difficult to bring into common use, owing to the opposi- 
tion of buyers who prefer lower standards even if inaccurate. 

The log rules whose use is sufficiently extensive to justify their con- 
sideration, on this basis alone, for universal adoption include only the 
following: 



Basis of Rule 


United States 


Canada 


Formula 


Doyle 


Doyle 

British Columbia 


Diagram 


Scribner 


Quebec 




Scribner Decimal C 


New Brunswick 




Spaulding 






Maine 




Hybrid 


Doyle-Scribiier 




Mill Tallies 


Massachusetts 





Of these, the Doyle must be rejected because of its glaring inconsis- 
tencies and the Doyle-Scribner because it combines the worst features 
of both rules. The use of the Maine and the Spaulding rules is confined 
to single states, and the Massachusetts rule is for a special form of 
product; i.e., round-edged timber. 

This leaves the Scribner, preferably in Decimal C form, as the only 
logical rule now in wide use, which is applicable to the measurement of 
square-edged lumber. 

If the admitted irregularities of the Scribner rule are deemed so seri- 
ous as to justify its rejection, its successor should not be chosen from 
among the other rules in common use, but should rather be a rule based 
on a formula and tested to conform to actual conditions of sawing. For 
such a purpose, the International {-inch Rule is probably as perfect a 



UNUSED AND OBSOLETE LOG RULES 85 

rule as will ever be required in commerce. This rule is especially valu- 
able for logs below 12 inches and above 28 inches, in which classes the 
Scribner rule is defective. There is nothing to be gained by further 
efforts to construct new " perfect " log rules. 

79. Unused and Obsolete Log Rules. In addition to the rules described in 
this chapter we may mention the following rule.s, all of which are now obsolete. 

Bangor Rule. Synonyms: Miller, Penobscot. The Bangor Rule was constructed 
from diagrams, and gives slightly higher and more consistent values than the Maine 
rule. It shows more care in construction and is probably the best of the diagram 
rules. Owing to the more extensive use of the Maine rule, this rule is almost obsolete. 

Parson's Rule. This rule is of similar construction to the Bangor and Maine 
rules and its values are almost identical but a little below the Maine rule. The 
difference is about 2 per cent. It is a local rule, still used to some extent. 

Boynton Rule, 1899 (Vermont, local). Made up from values taken from Scrib- 
ner and Vermont rules .checked by mill tallies. A fair rule but of no general value.. 
D. J. Bo3aiton, of Springfield, Vermont. 

Brubaker Rule. No detailed knowledge. 

Chapiii Rule, 1883. The most erratic of all log rules, made up apparently by 
selecting values from existing rules to suit the author. 

Dreiv Rule, 1896. The Drew rule has been the statute log rule of the State of 
Washington since 1898 but is used practically nowhere in the state. Instead, the 
Scribner rule is universally used, except along the Columbia River, where the Spauld- 
ing rule is in use. 

This rule (by Fred Drew, Port Gamble, Wash.) was made from diagrams checked 
by tallies of logs as sawed. The values are given for diameters from 12 to 60 inches 
and lengths of from 20 to 48 feet. Taper is not considered. The values are said 
to have been reduced to allow for hidden defects. The rule is inconsistent in scale, 
resembling the Doyle in tendency on large logs. Its use is practically discontinued. 

Dusenherry Rule, 18.3.5. This nilo was made in 1835 by a Mr. May, and adopted 
by Dusenberry-Wheeler Co., of Portville, N. Y. It was probably constructed 
from mill tallies, and was intended to measure the output of pine sawed If inches 
thick with some 1^- and 2-inch pieces. The saw kerf was j^ inch. The rule is 
very consistent and was generally adopted in the Alleghany Waters in Penn- 
sylvania. It is still used in that and adjoming states. Owing to the wide saw 
kerf used, this rule under-scales Scribner from 15 to 20 per cent and is not suited 
to present conditions. 

Favorite Rule. Synonym: Lumberman's Favorite A diagram rule, made 
by W. B. Judson in 1877 and published in Lumberman's Handbook, 1880. The 
values for small logs are lower by 15 per cent than Scribner's. The rule is now 
practically obsolete. 

Finch and Apgar Rule. Date unknown. A diagram rule, erratic, for i^-inch 
saw kerf. Gives low values. 

Forty Five Rule. About 1870. Based on an inaccurate rule of thumb formula 
which gives high values for small and large logs and low values between these 
extremes. 

Herring Rule, 1871. Synonym: Beaumont. The values in the Herring rule 
as originally made, to include from 12- to 44-inch logs, are practically identical 
with the Dusenberry rule. The rule was applied at the small end to logs up to 
20 feet in length. Above 20 feet a rise of 1 inch was added, and was applied at 
middle point of logs up to 40 feet in length. Here another inch was added, and the 



86 THE CONSTRUCTION OF LOG RULES 

scale carried to 60-foot logs. The taper allowed in this was is about half of the 
average taper. 

The rule is used extensively in the pine regions of Texas and gives a large over- 
run. 

The same trouble was ex-perienced with this rule as with the Scribner^ in agreeing 
upon an extension of values to cover logs less than 12 inches in diameter. The 
values most commonly used are the so-called Devant extension, based upon the 
Orange River rule, and agreeing closely with the Scribner extension. 

Licking River Rule. No detailed knowledge. 

Northwestern Rule. A diagram rule for |-inch saw kerf. Erratic, and similar 
to Scribner's. 

Ropp's Rule. A rule published by C. Ropp & Sons, Chicago. Based originally 
on diagrams of 1-inch lumber for a j-inch saw kerf, it was reduced to a rule of 
thumb which gives erroneous results especially for small logs, which are severely 
under-scaled. The rule is therefore of no value. 

Warner Rule. A diagram rule with excessive allowance of f inch for saw kerf. 
Worthless. 

Wheeler Rule. No detailed knowledge. 

Wilcox Rule. A diagram rule for f-inch saw kerf. Irregular. Low values. 

Younglove Rule.^ Fitchburg, Mass., 1840. A cahper rule resembling the Baxter 
in values. 

References 

General Treatises on Log Rules 

Relative Value of Round and Sawn Timber, James Rait, p. 114, Wm. Blackwood 

Sons, London, 1862. 
The Measurement of Saw Logs (Universal Rule), A. L. Daniels, Bui. 102 Vermont 

Exp. Sta., 1903. 
The Measurement of Saw Logs and Roimd Timber (Champlain Rule), A. L. Daniels, 

Forestry Quarterly, Vol. Ill, 1905, p. 339. 
The Measurement of Saw Logs (International Rule), Judson F. Clark, Forestry 

Quarterly, Vol. IV, 1906, p. 79. 
The Standardizing of Log Measures, E. A. Ziegler, Proc. Soc. Am. Foresters, 

Vol. IV, 1909, p. 172. 
The Log Scale in Theory and Practice (Tiemann Log Rule), H. D. Tiemann, Proc. 

Soc. Am. Foresters, Vol. V, 1910, p. 18. 
A Discussion of Log Rules, H. E. McKenzie, Bui. 5, California State Board of 

Forestry, 1915. 
Review of Bui. 5, California State Board of Forestry, by H. D. Tiemann. Proc. 
Soc. Am. Foresters, Vol. XI, 1916, p. 93. 

Specific Log Rules 

Scribner's Log and Lumber Book (Cubic Measure, Two-thirds Rule, Doyle Rule), 

S. E. Fisher, Rochester, N. Y., 1900. 
Extending a Log Rule (Devant Extension of Herring Rule vs. Doyle Rule), E. A. 

BranifT, Forestry Quarterly, Vol. VI, 1908, p. 47. 
Report of Commission to Investigate Methods of Scaling Logs in Maine (Holland 

Rule, Blodgett Rule, HoUingsworth & Whitney Rule), House Document No. 43, 

74th Legislature, Maine, 1909. 

1 Reference, Forestry Quarterly, Vol. XII, 1914, p. 395. 



UNUSED AND OBSOLETE LOG RULES 87 

A Comparison of the Maine and Blodgett Log Rules, Irving G. Stetson, Forestry 

Quarterly, Vol. VIII, 1910, p. 427. 
Woodsman's Handbook, Henry S. Graves and E. A. Ziegler (Scribner Decimal C, 

Doyle, Inscribed Square Log Rules, and Table of Comparisons of 44 log rules 

for 16-foot logs), Bui. 36, U. S. Dept. Agr. Forest Service, 1910. 
Comparative Study of Log Rules (Champ lain, Vermont and Doyle Rules), Austin 

F. Hawes, Bull. 161, Vermont Agr. Exp. Sta., Fart II, 1912. 

Log Rules Based on Mill Tallies 

Log Rules for Second-growth Hardwood from Mill Tallies, j-inch Saw Kerf, 

Round-edged Boards cut 1^ indies thick. Based on Small End, Inside Bark, 

and on Middle Diameter Outside Bark, C. A. Lyford, Reports of Forestry 

Commission, N. H., 1905 and 1907. 
Log Rule for White Pine, from Mill Tallies, J-inch Saw Kerf, for 60 per cent Roimd- 

edged, 40 per cent Square-edged Boards, 70 per cent l-inch Lumber, remainder 

2|-mch Plank, C. A. Lyford, Reports of Forestry Commission, New Hampshire, 

1905 and 1907. 
Log Rules for r2-ft. logs from Mill Tallies of Round and Square Edge Lumber, 

separately for White Pine, and Hardwoods, L. Margolin, Proc. Soc. Am. 

Foresters, Vol. IV, 1909, p. 182. 
Comparison of Round-edged and Square-edged Sawing for 2g-Lnch planks, H. O. 

Cook, Forest Mensuration of White Pme in Mass., 1908, pp. 38-43. 
Contrast of Output by Different Methods of Sawing, H. D. Tiemann, Proc. Soc. 

Am. Foresters, Vol. IV, 1909, p. 173. 
Log Rule for Hickories, in Cubic Feet, Bui. 80, Forest Service, 1910, p. 39. 
Log Rule for Hardwood Logs from Mill Tally, Yellow Birch, Maple, Beech, I. W. 

Bailey and P. C. Heald, Forestry Quarterly, Vol. XII, 1914, p. 17. 
Log Rule for Loblolly Pine, based on Mill Tallies, Logs with less than 2-inch Crook, 

i-inch Kerf. W. W. Ashe, Table 23a. Bui. 24, North CaroUna Geological 

Survey, 1915, p. 76. 



CHAPTER VII 
LOG SCALING FOR BOARD MEASURE 

80. The Log Scale. The scale of a given quantity of logs is their 
total contents expressed in the unit of measurement employed. The 
term " scale " also refers to the general rules or customs of scaling 
adopted in a given region or locality, upon which depend the liJ)erality 
or closeness of the measurement (§ 83). Differences in the method of 
scaling may make from 5 to 50 per cent difference in the scaled contents 
of the same logs (Table XVII). 

To determine the contents of logs in board feet, the diameter of the 
log is measured with a stick marked in inches, the length in feet is deter- 
mined by measuring it with the above stick or by a tape or wheel 
(§ 34), and the volume corresponding to these dimensions looked up in 
the log rule.^ This process is simplified by placing upon the sides and 
edges of this stick, opposite each diameter, rows of figures giving the 
values of the rule for each of several standard lengths. The volume in 
board feet is then read directly from the stick, and recorded. A stick 
so graduated is termed a scale stick or scale rule. 

Scale sticks are made of hickory or maple about 1 by J inch in cross section, 
graduated in inches, with the figures burnt into the wood (Fig. 10). Metal sticks 
are also in use and in some regions caliper rules are used. The inch scale is on 
one or both edges and the stick easily accommodates six or seven other rows of 
figures corresponding to the contents in board feet of logs of as many different 
standard 2-foot lengths. A metal tip aids in measuring the diameter inside the 
bark. Other forms are made for scaling logs in water, or logs with ends rounded 
or sniped. Lengths of scale sticks in inches correspond to the maximum diameters 
of the logs to be scaled. Hexagonal scale sticks are sometimes used. Scale sticks 
have been made. which are graduated at points giving volumes to exact tens or 
hundreds of units, but these rules have never become popular as the basis of the 
rule is not indicated (§ 111). 

The purpose of a log scale depends upon the ownership of the timber 
or logs. Where the logs are to be sold the scale is the basis of settle- 
ment and must be far more carefully made than when the timber is 

1 Experienced scalers sometimes substitute ocular or paced lengths on short 
logs. The scale of logs shorter than the minimum length given in the rule is taken 
as equaling one- half the scale of a log twice as long as the one in question, i.e., 
when the shortest length given on the scale is 10 feet, an 8-foot log is scaled as 
one-half of a 16-foot log. 

88 



THE LOG SCALE 



89 



owned, logged and manufactured by the same firm. In the latter case, 
the purpose of the scale is merel.y to provide a basis for the payment 
of contractors for logging or sawyers for felling, or for checking the com- 




-— ■ 8 



SCRIBNE8 
SCALE 



-28 _ 



Fig. 10. — Forms of scale sticks in use. 



parative efficiency of crews or camps. Finally, the woods scale deter- 
mines the quantity of timber felled, thus keeping track of the operation, 
while a re-scale at the mill permits the keeping of costs and credits 
separately, on the basis of the volume of logs delivered, between the 



90 



LOG SCALING FOR BOARD MEASURE 



logging and milling ends of the business, as if they were under separate 
management. Woods scaling also checks the accuracy of timber esti- 
mates, whenever the timber from given areas is scaled separately in 
logging. 

When the purpose is to determine the basis for paying saw crews, logs are 
scaled in the woods before skidding. When standing timber is sold on the basis 
of the log scale, the scaling is done at the skidways or landings before removal 
from the tract or vicinity. The mi.xing of logs cut from two or more tracts must 
be avoided by any necessary measure such as sawyers' marks, or scahng in the 
woods. Where no question of sale is involved, the logs are scaled wherever it is 
most convenient. Logs are usually re-scaled on the log deck. Where logs are 
rafted and sold, they usually are scaled in the water. 

81. The Cylinder as the Standard of Scaling. A log rule does not 
give an exact scale of lumber which will be or can be sawed from logs 

(§ 46). The log rule is an arbitrary 
standard fixing the quantity of 1-inch 
lumber said to be contained in logs of given 
diameters and lengths. When the top or 
small end of the log inside the bark deter- 
mines the diameter, as it does for all board- 
foot log rules in common use, these rules do 
not include any boards or pieces sawed 
from the taper or swell of the log. The 
scaler must therefore pay no attention to 
that portion of the contents of the log 
which lies outside of this cylinder, no 
matter whether this portion be sound or 
defective. On the butt end of a log, the 
contents to be scaled lies within a smaller 
circle representing the area of the top end 
of the log, or the cross-section of the 
cylinder whose diameter is this top end. 
This cylinder must coincide in position 
with the axis of the log, so that the center 
of the cross-section or area to be scaled 
coincides with the center of the butt or 
larger end of the log. Common errors in scaling are the shifting of the 
scaled cylinder towards one side to avoid defects, and the offsetting of 
defects within the cylinder against sound short lumber which may be 
scaled from the taper. 

82. Deductions from Sound Scale versus Over-run. Log rules 
give the scale of this cylinder in sound lumber and do not allow for 
defects. The standard scaling practice is to make deductions from 




Fig. 11. — Projection of area 
of top end of log on butt 
section, showing portion of 
butt to be scaled. The 
circle A represents the area 
to be scaled. The presence 
of defect in area C does not 
justify the shifting of this 
circle to position B but de- 
ductions for defect must be 
made from A. D is the 
geometric center of the log 
and of the scaled area A . 



SCALING PRACTICE 91 

the scale for all visible defects which lie within the cylinder in each 
log separately, of the amount of lumber which would be lost because of 
the defect. 

This rule is not always observed. In many species, certain defects may exist 
without visible external indications either on the surface or at the exposed ends. 
When the logs are in water it is difficult to detect defects. There has been a 
tendency on the part of makers of log rules to reduce the standard volumes of the 
log rule in order to offset these invisible defects (Scribner rule, § 68). Log rules, 
like the Cumberland River rule which gives but 45 per cent of the cubic contents, 
permit the buyer to ignore most defects with perfect safety. 

The use of a log rule which is known to give a large over-run (§ 47) usually 
gives rise to the practice of scaling "sound" and ignoring defects. The buyer 
can afford to be lenient, and the seller objects to any further discounts than those 
inherent in the rule itself. 

Except for a few species and regions, defects may usually be seen and 
deducted. Where the opposite is true, custom sometimes permits a 
reduction of the final scale by a straight per cent to allow for such 
invisible defects. 

Over-run (§ 46) is therefore an element which should not influence 
in any way the practice of log scaling. Where an admittedly defective 
rule is offset by lenient but inaccurate scaling practice, the entire 
technique and standard of scaling suffers, and such conditions should 
sooner or later yield to accurate standards, both in the rule used and 
in its application. 

83. Scaling Practice, Based on Measurement of Diameter at Small 
End of Log. The advantages of measurement of the log at the small 
end, which have made this custom practically universal in scaling, are 
that the scaling diameter inside the bark can be directly measured 
without guessing at bark thickness, and no matter how high a skidway 
or rollway is piled, the ends of the logs are usually visible for scaling. 
By contrast, logs to be calipered at the middle point can be measured 
only when lying separately or before being placed on rollways, and the 
bark thickness is usually guessed at. 

The per cent of over-run on the log scale is affected by three main 
factors. Two of these, namely, the elements affecting manufacture of 
lumber and the character of the log rule itself, have been discussed in 
Chapter V. The third is the practice of scaling, and the customs which 
govern it, collectively termed the " scale." This practice affects, first, 
the method of determining scaling diameters and lengths, for when 
these are once ascertained the rule permits no variation in contents for 
sound logs; and second, the deductions from this scale for defects, as 
interpreted by the scaler. 

Scaling Lengths. The total length of a log must be accurately deter- 
mined. For log rules which are based on diameter at the small end, 



92 LOG SCALING FOR BOARD MEASURE 

logs whose length exceeds a given maximum are scaled as two or more 
sections or shorter logs (§ 43). Custom or " scale " determines the 
maximum length to be scaled as one section and the method of deter- 
mining the taper or diameter of the second or remaining sections to be 
scaled. Short sections scaled to full or actual top diameter give the 
maximum scale, while the loss from scaling long logs as one piece based 
on diameter at top end may be very large, due to the increasing per cent 
of volume in long logs which lies outside the cylinder and is thrown into 
the over-run. 

The standard lengths of softwood or coniferous logs are multiples of 
2 feet, to which is added an allowance for trimming. Where long logs 
are divided into two or more lengths for scaling, this rule is still adhered 
to; e.g., a 26-foot log is scaled as a 14- and a 12-foot. Usually the 
longer length is scaled as the butt log. 

The tremendous variations in scale which may result from different 
treatment of scaling lengths and taper in long logs is illustrated in Table 
V (§ 44). In order to secure a consistent scale between long and short 
logs, the scaling length should be limited to not over 16 feet, and the 
actual diameter of each section taken as the scaling diameter. 

Trimming Allowance. The trimming allowance varies according to the method 
of transportation used. For logs hauled by rail or driven down sluggish streams, 
from 2 to 3 inches is allowed for each 16 feet of length. Large logs require the 
greater allowance, to guard against slanting cross cuts which might give a short 
length on one side. Where logs are driven down swift rocky streams the trimming 
length must be sufficient to allow for the brooming of the ends. In very bad waters, 
the exact length of a log is immaterial and the loss from brooming a heavy item. 
Odd lengths, i.e., lengths measured in odd feet as 13 feet, are permitted in hard- 
woods and to a limited extent in softwoods. 

In ordinary scaling, trimming lengths in excess of standard 2-foot gradations 
are not scaled. But sellers of logs, to reduce loss from careless cutting of log lengths, 
may stipulate that when trimming lengths are in excess of the margin agreed 
upon, the log shall be scaled as if cut from 1 to 2 feet longer. The U. S. Forest 
Service adopts this practice as a penalty scale. 

Scaling Diameters. In the apparently simple process of measuring 
the diameter inside the bark at the top end of the log, there are two ways 
in which the buyer may be given the advantage of a smaller scale. Owing 
to the irregular cross sections of logs, an average diameter should be 
found by taking two measurements at right angles. Instead, the 
practice of scaling the smallest diameter is common. The difference, 
in large logs, sometimes amounts to 2 or 3 inches. The second choice 
lies in the treatment of fractional inches. These fractions should be 
rounded off to the nearest inch; e.g., the 18-inch log class should include 
diameters from 17.6 inches to 18.5 inches. Instead, all fractions may 



SCALING PRACTICE 



93 



be dropped, throwing logs from 17.6 inches to 17.9 inches into the 17- 
inch instead of the 18-inch class. ^ 

The variations in scaling practice or local "scale" for the different regions in 
the United States and Canada are shown in Table XVII, p. 94. 

It is seen that the standard set by the U. S. Forest Service is almost nowhere 
complied with m private operations, and that the departures from this standard 
work uniformly in favor of the buyer. Except for hardwoods, there is no vaUd 
reason for rejecting fractional inches, since these are in most instances already 
rejected in the construction of the log rule itself (Scribner, § 68), and in any case, 
the contents of logs of exact inch diameters represent a fair average for logs varying 
up to J inch larger or smaller. In the same way, it is unfair to measure the 
smallest diameter instead of the average, for the sawed contents of logs with 
eccentric cross-sections is little if any less than for round logs, and certainly 
does not diminish in proportion to the ratio between smallest and average diameter.^ 




Fig. 12. — Effect of rapid taper at small end upon scaling diameter and 
scaled contents of a log. 



' The adoption of these two buyers' practices in the scale will result in a loss 
to the seller which, l^^y the Scribner log rule, amounts to from 5 to 15 per cent, 
averaging 8 per cent for logs rmining 10 to the thousand board feet, and 13 per 
cent for logs running 20 per thousand. The use of the average diameter, and the 
rounding off of fractional inches are practices fair alike to buyer and seller, and 
are required by the U. S. Forest Service in selling public timber. 

The practice of reducing unit feet in a log rule to tens, or converting the rule 
into a "decimal" rule gives a third opportunity for discrimination in favor of 
the buyer. The correct method is that employed in the Scribner Decimal rule where 
all fractions above 5 feet are thrown to the 10-foot value above, while those less than 
5 feet are dropped. But in one section of Maine it is the custom to drop all unit 
feet scaled by the Maine rule. Thus a log scaling 19 feet would be entered as 
10 feet. The effect of such a custom on the scale is self evident. 

^ In a contract for sale of logs, the log rule to be used must be mentioned. 
The practice regarding scahng length, trimming allowance, method of measuring 
taper or rise on logs of greater than scaling lengths, measurement of diameter and 
treatment fractional inches should be specified. Otherwise, common custom or 
scale in the locality will determine what constitutes a proper method. The method 
of deducting for defects whether by each log separately or by a straight per cent 
should be agreed upon, and if possible, standard instructions adopted for culling 
defects. The minimum dimensions of a merchantable log should be defined, both 
as to length and diameter, and as to per cent of total scale which must be obtained 
after deducting for defects. 



94 



LOG SCALING FOR BOARD MEASURE 



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SCALING PRACTICE BASED ON MEASUREMENT OF DIAMETER 97 



Abnormal Diameters. The practice of basing the scaling diameter on that of 
the small end of the log, with its consequent disregard of taper, gives rise to diffi- 
culties on logs which taper rapidly at the small end, as for instance, rough or limby 
logs on the basis of their top diameters may result in loss of scale when in reality 
a greater volume of the tree has been utilized. Fig. 12, p. 93. 

By the International j-inch rule this log would scale, in actual diameter 



Length. 


Scaling diameter. 


Scale. 


Feet 


Inches 


Feet B.M. 


12 


12 


70 


14 


9 


45 


IG 


6 


20 



Rigid adherence to the scaling practice on such logs results in the refusal of 
contractors to cut them. There are two possible modifications of the end diameter 
rule which will meet this condition: First, to scale the log as a shorter log, at the 
point which will give the largest total scale, in the above instance at 12 feet giving 
a scale of 70 board feet; second, to scale it as two logs, including the short tapering 
portion as a separate piece from the main portion. In the above case, the 6-inch 
top, with a length of 4 feet would add one-fourth of the scale of a 16-foot log of 
that diameter, or 5 board feet, giving a total scale of 75 board feet. The latter 
method is the most equitable, otherwise there is no object to the contractor in 
going into the top to secure closer utilization. 

Abnormally large diameters, occurring at the small ends of logs are the result 
of cross cutting through crotches or swellings caused by limbs, or by defects or 
cankers. Such diameters must always be reduced to a size representing the normal 
diameter of the cross section as determined by average taper. For slight swellings 
this is judged by eye. For crotches, the diameter at butt end is sometimes taken 
and average taper deducted. ' 

84. Scaling Practice Based on Measurement of Diameter at Middle, 
of Log or Caliper Scale. None of the true board-foot log rules in common 
use are applied at the middle of the log. By the Blodgett Rule, a cubic 
rule expressed in board feet (§ 33) the log is usually measured in the 
middle, outside the bark. When taper is taken on long logs by the ordi- 
nary rules, the scaler depends upon his scale stick and ocular judgment 
for the measurement of the upper diameters. But if logs are customarily 
cut long, and must be scaled by getting actual taper rather than assumed 

1 The following court decisions are important as defining the bearing of the 
"scale" on agreements: 

"In the absence of any agreed standard of measure in a contract, that of the 
place where a commodity is purchased will govern the contract." Supreme Court 
of New York, Dunberic vs. Spaubenberg, 121 N. Y. 299. 

"Where a contract involves the measurement of logs by specified rule, but 
does not indicate the manner of measuring whether by end, average or middle 
diameter, local custom shall determine such manner." Supreme Court of Louisiana, 
13 So. 230. 



98 LOG SCALING FOR BOARD MEASURE 

standard tapers, calipers must be brought into use in scaling. The 
calipers employed in scaling logs by the Blodgett rule are equipped with 
a wheel of 10 spokes, one revolution measuring 5 feet in length (§ 34). 

The greatest drawback to a caliper scale is the necessity of determin- 
ing the width of bark, doubling this, and subtracting to get the scaling 
diameter of the log. When all logs are calipered, it is a common prac- 
tice to determine the average width of bark of the species and region, 
and deduct twice this fixed amount on all logs regardless of variations 
in actual bark thickness, relying on the law of averages to secure a true 
scale. For the Blodgett rule, f-inch for each bark is allowed and the 
calipers are adjusted to read the diameter inside bark direct. On the 
Big Sandy River in Kentucky (Big Sandy Cube Rule) the allowance is 
1 inch for each bark.^ 

85. Scale Records. The tally is the record kept of the logs by the scaler or his 
assistant, the tally man.^ The tally may consist merely of a record of diameter 
and length of each log. From this the full scale is easily computed at camp. But 
the system prevents deductions for defects from each log separately, and is used 
only where such discounts are not made, or are made either as a per cent of total 
scale, or by reducing the length or diameter of the log. This primitive method 
of scahng has been largely replaced by the plan of recording the board-foot contents 
of each log when scaled. From the full scale, deduction is made for defect, and the 
net or sound scale recorded. For long logs scaled in two or more sections, only 
the sum of these volumes is set down, giving the total scale for the log as one piece 
and thus keeping the count intact. The purpose in this is to obtain a tally of 
the exact number of pieces scaled as well as their total contents. 

To still further insure an accurate record, logs are numbered serially, with 
crayon, coinciding with printed numbers in the scale-book. This enables a check 
scaler to re-scale and compare individual logs, or any number of logs, with the 
original scale to determine the per cent of error and the specific faults in practice. 
Without such enumeration, the entire number must be re-scaled to obtain a check, 
and specific errors are not shown. The method of numbering is cumbersome where 
large quantities of very small logs are handled, but it is the only plan by which a 
uniform standard of scaling may be attained by a force of several scalers. 

1 A second method, employed in Maine in scaling cubic contents, is to assume 
that the volume of bark is I25 per cent of the total volume of the tree with bark. 
The diameter outside bark is measured direct, and the volumes given on the rule 
are computed to express the contents of wood alone. 

Bark is never removed, in scaling, to permit the calipering of the direct measure- 
ment inside bark, as this process is too time consuming. The Tiemann log rule 
(§ 63) which applie.s to middle diameter inside bark, if used commercially, would 
probably be applied by the common method of deducting fixed widths of bark, 
to be regulated by measurements taken of the species and locality. This practice 
permits of an additional source of variation in measuring diameters (§ 29) through 
the bark on individual logs being thicker or thinner than the arbitrary measure- 
ment. 

2 Scalers usually work alone, preferring the extra labor to the risk of errors 
made in the record by incompetent tally men. 



SCALE RECORDS 99 

The scaler marks the logs with crayon as he scales them. If not numbered, 
they are check marked. 

Where logs are piled in rollways, unevenly, and cut different lengths, the count 
must be checked carefully to see that none is missed. This is best done by making 
a recount after scahng a rollway, and check marking the butts of the logs, the 
tops having been marked in the scaling. Logs piled in high rollways can best be 
scaled by two men, one working at each side of the rollway. 

Cull logs which are not scaled are given a distinguishing mark. If already 
skidded, they should be counted and recorded as culls. The scaling of logs in 
the woods eliminates the culls from the scale altogether and saves the expense of 
logging them. 

Log Brands, Termed Stamps and Bark Marks. When the practice is necessary 
the scaler must see that the logs have been properly stamped and bark marked. 
A stamp is a pattern or die stamped into the end of a log with a marking hammer. 
A bark mark is a pattern cut into the bark, usually near an end, with an axe. 
Stamps and bark marks are used to distinguish logs when driven with those of 
other owners down a common stream. These marks are recorded by scalers and 
determine the ownership of the logs. 

The Scale Book. A form of scale book is shown on p. 100 containing 100 printed 
numbers on a page with spaces for entering the contents of logs, and for totaling 
each column separately and adding these totals for the page. 

The scale record shown in this sample page is for the Scribner Decimal C Scale. 
The original records give the scale in tens of feet. At the foot of each column, the 
total is entered parallel to the base, and the zero added to obtain full scale. 

Logs whose scale has been culled show the net scale, and also the amount 
culled enclosed in a circle as, (e), which permits checking the cull. 

Other forms of scale records are in use following these general principles.^ 

86. The Determination of What Constitutes a Merchantable Log. 

A merchantable log is one which it is profitable to log. Logs whose con- 
tents will not return the cost of logging and manufacture are unmer- 
chantable. This may be due either to small size, to defects which 
reduce the scaled contents of the log, or to high cost of logging. 

Minimum Size. The costs of producing lumber are separated into 
logging cost and milling cost. Both depend on the cubic volume of the 
log. But both are modified by the time required in handling separate 
pieces. This causes the cost per cubic foot to increase for small logs. 
In logging, and in small mills, the cost also increases per cubic foot when 
logs reach large sizes difficult to handle. 

The value of the product depends not upon the cubic contents of 
the log, but on the quantity of sawed lumber which it contains, and 

1 The following court decisions are of interest: "When record of scale is kept 
on temporary paper and transferred every evening to permanent record, this 
record holds in court as original evidence." Court of Appeals, Alabama, 68 South. 
698. 

The U. S. Forest Service instructs its scalers to make the original and final 
record of scale in the field because of the HabiUty of error in copying figures. 

"Parties must abide by the official scaler's report except that fraud or gross 
mistake can be shown." Supreme Court, Michigan, Brook vs. Bellows, 146 N. W. 311. 



A. 

. 7S70 




100 LOG SCALING FOR BOARD MEASURE 

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WHAT CONSTITUTES A MERCHANTABLE LOG 101 

finally, upon the qualities or grades, and price of this lumber. The 
ratio of board feet per cubic foot (§ 41), the quality and value, all 
increase with increasing size of log. Due to these factors, logs below a 
given diameter and length, or total scale, even if sound, become unprofit- 
able or unmerchantable. This minimum diameter and length, when 
specified, relieves the logger or purchaser of the requirement of remov- 
ing such logs from the woods, cutting them from tops, or felling trees 
which will not yield larger sizes. If he chooses to take these sizes, 
especially from the tops, the logs are customarily scaled and paid for. 

Defective Logs. Defective logs, which will produce only a portion of 
the normal contents of sound logs of the same size, cost just as much to 
log and saw as if sound. But the ratio of lumber secured per cubic 
foot is reduced in proportion to the amount of cull, and the margin 
between cost and value shrinks accordingly, until it disappears and the 
log is classed as a cull and not scaled even if taken by the logger. Defects 
occur most frequently in large logs, whose quality and value are high. 

A defective log which produces a small per cent of its contents but 
of clear lumber or high grades may be merchantable, while a rough log 
with a much smaller per cent of defect may not show a profit in handling. 
Millmen who log their own timber can base their standard for culls 
directly upon this margin of profit, and can afford to accept very defect- 
ive logs for a few high-grade boards. Value or margin of profit, if 
applied as a standard in selecting or rejecting logs, means an elastic 
per cent of cull dependent on the character of the log itself. But the 
logger or logging contractor is paid not by value or grade of sawed lum- 
ber, but by the scale. Since his costs are determined by cubic volume 
and size, he would prefer a cubic log scale, but in accepting payment on 
the basis of board-foot contents, his profit in logging depends instead on 
the ratio of board feet to cubic feet independent of quality, and is 
diminished by reduction in scale caused by cull. On the other hand 
the loggers' costs vary with the distance which the log must be skidded 
or hauled. A log with a given per cent of sound scale if near the point 
of delivery will show a profit, while the same log is unmerchantable if 
located at a greater distance from the track. For defective logs, then, 
the merchantability is determined, for the millman, by comparing the 
combined cost of logging and milling with the value of the product, 
but for the logger it is determined by comparing the price per thou- 
sand board feet secured for the scaled contents of the log with the cost 
of delivering it to the point agreed upon. 

Where firms are doing their own logging, sawyers and loggers are 
frequently paid on basis of full scale disregarding cull. But in contract 
logging, the scaler usually rejects cull, thus requiring an agreement on 
the per cent of sound contents which constitutes a merchantable log. 



102 



LOG SCALING FOR BOARD MEASURE 



This per cent cannot be varied from log to log according to value of 
contents to favor the millman, or to location of log to favor the logger, 
but is arbitrarily set at an average figure applicable to all logs of a given 
species. Different per cents are permitted for species having different 
average values, the greater the value the lower the per cent of sound 
lumber accepted. As between the logger and the millman, the use of 
the board-foot scale favors the latter, but its application regardless of 
grades of lumber in the log is a concession to the logger. The rejection 
of cull logs is a concession to the millman but the adoption of a fixed, 
percentage for each species simplifies administration and aids the logger, 
who does not have to determine the profit in a log but only the cost of 
logging. Contract loggers are favored, then, by a cubic basis, no 
deductions for cull, and reduction of logging costs by leaving inaccess- 
ible logs in the woods. The manufacturer considers the additional 
factor of profit or value of the log, which the logger himself would 
have to consider if he were selling his logs. Only by determining aver- 
age total costs and average values for a given logging operation can 
the actual specifications of a merchantable log be determined, and the 
average agreed upon. In the U. S. Forest Service the custom is quite 
widely adopted that logs of the more valuable species must scale 33^ 
per cent of their sound contents, and those of inferior species, 50 per 
cent to be merchantable. 

The limits of merchantability will vary widely in every region, unless standard- 
ized as is the case in the Pacific Northwest. The average conditions for different 
regions for the year 1917 are indicated below: 



Region 


Smallest diameter. 
Inches 


Per cent of sound 
scale accepted 


Central, hardwoods 


8 to 12 
7 to 8 

4 to 5 . 

5 to 8 

12 

6 to 9 


40 to 70, average 60 
25 to 75, average 50 
10 to 25, average 20 
20 to 33, average 25 
33 i 


Southern pine 

White pine. Lake States 


Idaho 


Pacific Northwest 


Southwest 


30 to 40, average 33 



These limits apply to saw logs. For pulpwood, bolts are taken down to between 
3 and 4 mches. 

Tests on spruce logs in the Adirondacks showed that 5-inch logs had a relative 
value per board foot of 56 per cent compared with 11-inch logs at 100 per cent, 
while the relative value of 20-inch logs was 126 per cent.' 



' The following legal decision is interesting: 

"A merchantable log is one that contains sufficient lumber to make it profitable 



GRADES OF LUMBER AND LOG GRADES. 103 

87. Grades of Lumber and Log Grades.^ In the scaling of logs 
the primary object is to determine the contents in board feet of sound 
lumber as fixed by the arbitrary standard of the log rule, based solely 
on dimensions of the log, and modified only by deductions for unsound 
lumber (Chapter VIII). 

But as shown in § 86, the purchaser of logs, or millman, is even 
' more concerned with the value per 1000 board feet of the scaled contents. 
This value will depend directly upon the amount, by per cent of the 
total scale, of each of several standard or recognized grades of lumber 
which the logs will yield when sawed, and the resultant weighted aver- 
age value which this gives to the logs as a whole. 

When the value of logs must be determined before sawing, as is 
required when logs are purchased, and in the sale of standing timber, 
the relative percentages of these standard grades which will probably be 
produced from these logs or the stands in question must be estimated. 
It is evident that this can only be done with approximate accuracy, 
since a mere inspection of the surface and ends of logs will not reveal 
exactly the condition of the interior as to texture, extent of defects 
and per cent of better and poorer grades present. 

In scaling, no attempt is ever made to divide or separate the total 
scale of a log as indicated by the log rule, into the amounts or per cents 
of different grades of lumber in the log. Not only would such a process 
be too expensive and time consuming, but it would not be sufficiently 
exact to pay for the effort of calculating the results separately log by 
log to get the total scale for each grade of lumber. 

Instead, a system has been substituted of establishing so-called log 
grades, usually three in number, based on the average value of the con- 
tents of logs as determined by the grades of lumber which they contain. 
This classification permits of the fixing of separate prices for each log 
grade. The total scale of each log is thrown to the log grade in which 
it is classed. 

Defects in lumber (§ 352-353) may be separated into two classes, 
unsound defects which reduce the scale of the log as described above, and 
sound defects which reduce the grades of sound lumber but do not reduce 
the scale of the log. The effect of the first class is to render the log 
unmerchantable if in excess of the determined limit; the effect of the 
second class is to lower the value and consequently the grade of the 

to take it to a mill and have it sawed." Gordon vs. Cleveland Sawmill Co., 82 
N. W. Rep. 230, Supreme Court, Michigan. 

This ruling is based on the millman's point of view, which, in the absence of 
contract specifications protecting the logger, will always determine the standard of 
merchantability. 

'■ Ref . Appendix A, 



104 LOG SCALING FOR BOARD MEASURE 

log. The fact that, with increasing prices unsound lumber is sold and 
is graded does not change the standard scaling practice, which takes 
no account of these unsound grades and excludes them from the scale. 
Such lumber merely increases the amount of the over-run. 

The characteristic sound defects are tight or sound knots, pitch 
and stain. Sound tight knots never reduce the scale unless present in 
such size and quantity as to cause the lumber to fall apart or to be 
rejected. Stained sap, which is still firm, or red heart, the precursor 
of red rot, are scaled. Pitch is usually classed as a sound defect for 
which no deduction in scale is made. But these defects, especially 
knots, and others such as twisted grain and wide rings do serve to reduce 
the grade of the log. The presence of unsound defects, such as rot, 
shake and break, does not reduce the grade of a log, provided there is 
sufficient sound lumber remaining to permit the log to meet the mini- 
mum requirements of the grade. Since the purpose of log grades 
is to establish value, log grading specifications are drawn so as to permit 
logs of the same average value to be placed in the same grade, and too 
detailed specifications are avoided. 

By thus simplifying the classification of logs by grade, the total 
log scale is easily separated into log grades, and any variation in the 
average quality of logs within the grade can be adjusted in the price 
of the grade (§ 359). 

For any given region, and class of timber, the actual average per 
cents of different standard grades of lumber contained in log grades 
can then be determined by mill-grade or mill-scale studies (§361). 
These per cents can then be applied to the total scale for each log grade 
with far greater accuracy than could be attained by attempting to ana- 
lyze the scale of each log. 

Log grades, as analyzed by such mill-grade studies, have become the 
basis of determining the stumpage value of standing timber in appraisals 
as conducted by the U. S. Forest Service (§ 234). 

References 

Cost of Logging Large and Small Timber, W. W. Ashe, Forestry Quarterly, Vol. XIV, 

1916, p. 441. 
Cost of Logging Small Timber, R. D. Forbes, American Lumberman, Nov. 15, 

1919, p. 52. 
Cost of Cutting Large and Small Timber, W. W. Ashe and R. C. Hall, Southern 

Lumberman, Dec. 16, 1916. 
Inland Empire Sawing and Skidding Studies, J. W. Girard, Timberman, September, 

1920. 



CHAPTER VIII 
THE SCALING OF DEFECTIVE LOGS 

88. Deductions from Scale for Unsound Defects. No deduction 
will be made from the scale of a log unless there is some visible indica- 
tion of unsound defect such as will reduce the quantity of sound lumber 
that can be sawed from the log. The character and extent of the deduc- 
tion to be made for the indicated defect is judged by the scaler based 
on his knowledge of the given species and region and his experience in 
observing .the way such logs open up in sawing. Defects visible at the 
ends of the log give a basis for judging the remaining contents. Wlien 
logs must be scaled as they lie after bucking, with ends still in contact, 
as sometimes happens with overhead skidder operations, it is difficult 
to make correct deductions for defects. 

The surface of the log offers additional evidence of unsound defects, 
especially -the character of the knots. Sound knots from live limbs 
do not affect the scale, but the knots of dead stubs, if they show rot, 
and especially the presence of rotten knot holes, with exudations of 
pitch, indicate the presence of advanced stages of rot, which a little 
experience in the mill will teach the scaler to allow for in full measure. 
The mere suspicion that logs may be rotten does not justify deductions. 
When timber is full of concealed defects with no surface indications, 
the method of deducting a given per cent of the total scale may be 
adopted instead of attempting to reduce the scale of each log sepai'ately. 

89. Methods of Making Deductions. There are four methods of 
reducing the scale of a log; by length, by diameter, by diagram or 
specific quantity of lumber and by a per cent of the gross scale. The 
reduction in either length or diameter enables the scaler to read the 
reduced scale from his stick as for a log of smaller dimensions and is 
the sunplest form of discount, but least accurate except for certain 
forms of defect. 

Reduction in Length. A redliction in length gives a proportionate 
reduction in per cent of total contents. The per cent taken depends 
on the relation between the lengths of the log before and after reduc- 
tion. For a 16-foot log, 12| per cent of the total scale is deducted 
for each 2-foot reduction. This deduction becomes 10 per cent for 
a 20-foot log or 16| per cent for a 12-foot log. 

Reduction in Diameter. Reduction in diameter is not a satisfactory 
method of making deductions except for rotten sap found on logs cut 

105 



106 



THE SCALING OF DEFECTIVE LOGS 



from dead trees, or for surface checking. The per cent of the scale 
thus deducted varies for every diameter of log, and for each difference 
in the number of inches subtracted. This method of deduction should 
not be used to offset some interior defect. By this method, a 20-inch 
log by Scribner's Rule would give the following deductions from scale 
in per cents. For other diameters, the per cents would differ: 



Reduction of 

diameter. 

Inches 


Per cent deduc- 
tion in diameter 


Per cent loss 
in scale 


1 
2 
3 
4 


5 
10 
15 
20 


14.2 
25.0 
36.7 

42.8 



This method should usually be rejected in favor of one of the other 
three, since it substitutes a guess for an accurate deduction. 

Use of Diagrams. The diagram method is the most accurate way 
of computing the actual number of board feet to deduct from a log 
for a given defect. The cross section of the defective area is blocked 
out as a square or rectangle, and its length decided upon, whether 
running completely through the log or only part way through. For 
rules based on ^-inch saw kerf, 20 per cent of the cross section of this 
area must be deducted to get the net volume of 1-inch boards to be 
deducted from the scale. 



This is expressed by formula when 
a -6 = cross sectional area in inches, 
i = length of defective section in feet, 
y = cubic contents of the section in board feet, 
a; = volume of section, sawed into 1-in. boards, j-in. saw kerf. 

a-h-l 



Then 



or 



y= 



12 



x = y- .207j= .80y, 
ah-l 



x = 



15 



In using a decimal rule, the resultant volume is rounded off to the 
nearest 10 or "decimal value" before subtracting it from the log scale. 



EFFECT OF MINIMUM DIMENSIONS 



107 



As a substitute for this calculation and to save time, scalers frequently 
approximate the amount of deduction by guess, based on experience. 

Deducting a Per Cent of Total Scale. The method of deducting a 
per cent of the total scale, as distinguished from the above methods 
is chiefly applied to logs containing defects within the log, evidenced 
by rotten knots, punk, conks, or other indications and whose amount 
can only be guessed at on the basis of experience obtained by observing 
such logs as they are sawed in a mill. 

Influence of Log Rule on Deductions for Defects. A log rule based either upon 
diagrams of 1-inch boards and definite saw kerf, or upon a formula in which the 
proper deductions are made both for saw kerf and slabbing, permits the scaler 
to make deductions from the scale of each log separately on the basis of the actual 
loss in 1-inch boards from that portion of the log included in the scale or log rule. 
But when a log rule is inaccurate, either because of excessively low valuations, 
false basis as in converted cubic rules, or erroneous values in formula? as in Doyle 
or Baxter rules, such deductions when applied to logs already scaled too low would 
take from the scale more than the proper per cent of defect, as the following com- 
parison will show. 

A log 10 inches in diameter and 16 feet long, which will saw out but one-half 
of its scaled contents due to defect (and omitting boards sawed from outside the 
cyHnder), if scaled by the Scribner and Doyle rules respectively will give: 



Log rule 


Sound 
scale. 

Feet B.M. 


If actual loss in 

sawed content 

is 

Feet B.M. 


Net scale 

deducting actual 

loss. 

Feet B.M. 


Net scale 

deducting 50 per 

cent of sound 

scale. 

Feet B.M. 


Scribner 

Doyle 


54 
36 


27 
27 


27 
9 


27 
18 



If the log is sawed by a mill whose output coincides with the Scribner rule, 
the over-run on a sound log by the Doyle rule will be 50 per cent. The defective 
log will give no over-run of sound lumber by Scribner. But if 27 feet, or one-half 
of the actual sawed contents, is deducted from the scale by Doyle rule the over-run 
will be 18 feet, which is 200 per cent of the residual scale of 9 feet, on this scale, or 
four times as great on the defective as on the sound log. By deducting 50 per cent 
of the Doyle scale for the log, the over-run remains at 50 per cent of the scale as 
for sound logs. 

Although the method last mentioned gives a consistent basis for making deduc- 
tions in rules like the Doyle, while the deduction of actual loss in lumber gives 
far too great an over-nm, it is evident that when log rules are used capable of giv- 
ing a scale equaling but two-thirds of the actual contents, the tendency will be to 
overlook the defects in scaling unless very serious and numerous. 

90. Effect of Minimum Dimensions of Merchantable Boards upon 
these Deductions. Log rules made from diagrams, such as the Scrib- 



108 



THE SCALING OF DEFECTIVE LOGS 




ner and Spaulding Rules, were based on a minimum width of board of 
not less than 6 inches. Present practice permits the sawing of 4-inch 
strips. In deducting for defects by diagram, the latter practice is 
used, and portions of the log which will yield 4-inch strips are scaled, 
provided these dimensions lie within the cylin- 
der and do not include taper. A rotten butt 
with 6 inches of sound wood will be a total cull 
unless the inscribed area of the top or small 
end of the log contains within it at least 4 inches 
of sound wood. 

In theory, this rule must be modified for 
deductions which take the form of slabs, since 
the original diagram or scale rejected all boards 
below 6 inches in width. This case is illustrated 
in Fig. 14. 

The minimum length of merchantable board 
should first be standardized or agreed on in 
scaling. Formerly a defect at one end of a 
standard log, say 16 feet long, would cull the 
boards affected for their whole length. But 
where boards of 6- or 8-foot length are merchant- 
able, defects which leave a sound length equal 
to these minimum boards will be scaled only 
for the actual length of the part affected. This 
rule affects the results for nearly all forms of 
defect. Standard minimum lengths are im- 
portant in scaling crooked logs. The standards 
now in use for saw timber vary from 6 to 10 
feet with a tendency to become shorter. 

91. Interior Defects. Unsound defects may 
be classed as interior, causing waste in the interior 
of log; side or exterior defects, causing waste 
at the surface or outside; and defects in form, 
i.e., crook, in otherwise sound logs, causing 
waste in sawing straight lumber. Interior defects are due to rot, 
shake, seams or checks, and worm-holes. The defect may extend 
through the entire log, or be present only at one end. It may be cir- 
cular, and regular in form, or irregular in form and extent. 

Center Rot. Circular defects in the form of either rotten or hollow 
logs, or ring shake, if they extend through the log, will be measured not 
at the small but at the large end, provided the log is not over 16 feet 
long. For longer logs the average of the dimensions at butt and top is 
taken. If only one end is affected, the diameter of the defective portion 



Fig. 14. — The boards 
lost are measured in- 
side the smaller in- 
scribed circle repre- 
senting the top diam- 
eter. Three boards 
are affected, 4 inches, 
6 inches, and 8 inches. 
The 6-inch board is 
deducted. If the min- 
imum width of board 
utilized is 4 inches, a 
4-inch strip is de- 
ducted from the 8-inch 
board. But the 4-inch 
strip on the margin 
was not scaled in the 
original diagram and 
should be omitted, as 
constituting over-run 
by this log rule. In 
ordinary scaling prac- 
tice this distinction 
would probably be 
overlooked as too 
great a refinement. 



INTERIOR DEFECTS 



109 



is scaled at that point and its length judged by experience gained in 
the locality by the butting off of defective logs; e.g., a log 20 inches in 
diameter at the top end, 16 feet long, with a center rot measuring 3 inches 
at top and 15 inches at butt, will lose the equivalent of a 15-inch butt rot, 
and not a 3-inch piece. Should the log be 20 feet long, the average 




Fig. IS.^When the minimum length of board is 8 feet this log will scale one- 
half of the contents of a 16-foot log. But with a minimum length board of 
10 feet the log according to common practice will scale nothing and be culled. 

dimension of this rot, or 9 inches, would be taken, according to the 
above arbitrary rule of scaling. But if the rot is present only in the 
butt, the 15-inch measurement would apply to that portion of tl\e log 
which was judged to be affected, provided the length of the remaining 
sound portion equaled the minimum length of board prescribed. 




Fig. 16. — Center rot extending through log. Effect of length of log in determining 
the diameter of the portion to be culled. 

The scale of this log, if sound, would be 280 board feet, Scribner Decimal C 
rule. The deduction for a rotten butt 15 inches in diameter and 16 feet long 
is 228 board feet, residue 52 board feet or 18.2 per cent of sound scale. The 
log is a cull. The average w dth of rim left to be scaled after projecting the 
area of the rotten butt upon the top end, is 2^ inches, or less than minimum 
width of board, and not the actual measurement of sound wood at either the top 
or the butt. 

If this log is 20 feet long, i.e., longer than a prescribed maximum length of 
16 feet, the diameter of this rot is averaged at 9 inches. The 20-foot log, 20 mches 
in diameter scales 350 board feet. The 9-inch measurement is applied to the 
entire length of log, and the deduction is 111 board feet. The net scale is 240 
board feetj or 68.6 per cent of total sound scale. Such a log is merchantable. 



110 THE SCALING OF DEFECTIVE LOGS 

It is evident that such rules for deductions are arbitrary. The 16-foot log 
would yield considerable short lumber and is under-scaled by the rule. Where 
short-length boards are commonly used, logs over 12 feet long might be scaled 
on the basis of average diameter of rot, to correct this tendency. But it is better 
to adopt arbitrary rules than to have no methodical plan for scaUng defects. 

The cull required by the presence of an unsound or hollow circular core is pro- 
portional to the diameter of the core, and independent of that of the log. By the 
diagram method, the deduction for center rot would be found by determining the 
board-foot contents of a square with the diameter of the rotten core and of the 
length indicated as above. This method when checked against actual sawed 
contents gives too smal a deduction for cores up to 9 inches, and above that, too 
large, the relation varying from 87 per cent for a 6-inch core to 110 per cent for 
one 24 inches in width. The actual amounts of sawed lumber lost for cores of 
each diameter are accurately expressed by a formula developed by H. D. Tiemann, 
which reads, 

L 

Contents of core = 3(D-|-l)^, 

i.e., add 1 inch to diameter of core, square and deduct \, converting the remainder 
into board feet by the factor 

Length in feet 
12 ■ 

This formula calls for four-fifths of the sawed board-foot contents of a square 
1 inch larger than the core (0.66^^ = 82.5 per cent or f of 0.80D-) instead of the 
full sawed board-foot contents of a square of the same size as the core. 

Several rules of thumb exist for determining the deduction for center rot, none 
of which are absolutely correct, and some very inaccurate. 

Example. In a r2-foot log 20 inches in diameter with a rotten center 6 inches 
in diameter at large end and running through the log and a sound scale of 210 
board feet, the correct deduction is 33 board feet which is f (7-)y^. The following 
rules of thumb can be cited, using Scribner Decimal C rule. 

1. Deduct the diameter of core from that of log, and scale as a log. This 
gives a cull of 90 board feet. 

2 Deduct the scale of a log of same diameter as the core. This gives a cull 
of 10 board feet. 

3. Scale out a log with diameter 3 inches larger than the core. This would give 
30 board feet, but the rule gives inconsistent results for larger and smaller cores. 

4. Scale out the contents of a square timber whose side is the diagonal of the 
square of the diameter of the core. This would be 1.4D- and gives 70 board feet. 
If reduced by 20 per cent for saw kerf, and applied to small end of core, it would 
come closer by balancing errors. None of these rules is accurate or consistent. 

Butt Rot, Termed also Ground or Stump Rot. Butt rot enters the 
butt log from the ground, and usually extends but a short distance into 
the log. Its full diameter should seldom be applied to the entire log, 
even if rot appears at the top end. 

The diameter of the rotten butt must first be compared with the 
scaling diameter as determined by the top end of log (§ 81). If the rim 
of sound wood lying within this inscribed circle is wide enough for boards, 



INTERIOR DEFECTS 111 

or if the volume of the rotten core, -^— ^ shows a smaller cull than the 

15 

sound scale of that part of the log, deduction by diagram of the squared 

core is made (preferably by Tiemann's formula) to a length judged to 

include the rotten portion. 

Example. A log 12 feet long and 20 inches in diameter at top end has a rotten 
butt 6 feet long, the rotten core measuring 17 mches across. Although the butt 
measures 25 inches, leaving a 4-inch rim of sound wood, the inscribed circle repre- 
senting the top of the log is only 20 inches, and the butt is a cull. This observation 
is borne out by applying Tiemann's formula: 

Scale of r2-foot log, 210 board feet, 

Scale of 6-foot length, 105 board feet, 

Cull for butt rot, |(182)y*V = 108 board feet, 

or more than the sound scale of butt. This deduction is not applied to the whole 
log but only to the butt. 

The scale of the log is then 105 board feet on the basis that the upper half is 
sound. 

If this core should measure 13 inches, 

Cull for butt rot i(142)y6__ = 65 board feet. 

The scale of the log is then 210 — 65 = 145 board feet. 

But if the minimum board length should be over 6 feet, the first log will be 
culled entirely, and from the second log, a cull of f(14-)Y|^ or 131 board feet 
Scribner Decimal C is deducted, leaving a scale of but 79 board feet, or 37.6 per 
cent of the merchantable contents. 

Shake. Shake is a mechanical defect caused by wind. The annual 
rings have separated at one or more points, giving a circular or ring crack, 
and the board falls to pieces when sawed. This flaw is found at the butts 
of such species as hemlock, and is seldom more than a few feet in length 
although entire logs may be shaky. Lumber sawed from shaky por- 
tions of logs is often worthless. 

A single circular shake is scaled out in the same manner as butt rot 
except that the contents of a smaller sound core Ijang within the shake 
may be added or restored to the scale. The diameter of this interior 
core should be measured at the small end of the culled section if it extends 
through the log, while the diameter of the culled portion is measured 
at the butt or large end. In short sections whose length is guessed at, 
a proportionate reduction from butt diameter is made in scaling the 
sound core. This same method is used to scale out pitch rings, where 
this is deemed necessary. In most cases pitch is considered a sound 
defect (§ 82). Where shake shows in several rings, the entire shaky 
portion of the log is butted, by shortening its length. 



112 



THE SCALING OF DEFECTIVE LOGS 



Seams, Heart Checks, Frost Cracks or Pitch Seams. Seams are cracks 
penetrating the log from the surface. They have the same effect as 
shake, in causing boards to fall apart, and the deduction is made by 
enclosing the seam in a timber of requked dimensions to remove it. 

Twisted grain, causing seams to take a 
spiral form, results in ruining either the 
entire log or a large per cent of its volume. 
The deduction must include the entire 
seam in a squared timber. The width of 
the plank deducted should not include the 
portion which would be slabbed in sawing. 
Method of deducting for a twisted seam 
or check: The wedge enclosing the seam is 
scaled as a per cent of total scale of cylinder 
proportional to areas of cross sections. 
Fig. 17. -Method of deduction g^^ ^^ ^^^^ j^gg^ ^f l^^^.g^j. diameters, the 

for a seam, or a heart check. .. ,, . ^. -,o- j. 

™, .,,, r 1 , u ij entne segment shown m Ing. 18 is not 
The width of plank should ° " 

exclude both the taper of log lost, if short boards of scahng length can 
and the slab, on the small end. be sawed from the butt and top portions 

of the segment respectively. This saving 

will not amount to more than one-third of the total deduction. 

Worm Holes. If the size and extent of worm holes is not sufficient to 

cull the boards, their presence will not cause a loss in scaling. It is 

difficult to judge the extent of damage from worm holes, except by local 

experience in observing the sawing of logs. 






Fig. 18. — Position of twisted seam at butt, and at top of same log, and resultant 
sector deducted in scaling. 

Rot Entering from Knots. The most common forms of rot enter 
the tree through dead limbs, stubs or knots, or through wounds or abra- 
sions, which by penetrating or interrupting the layer of bark and live 
sapwood, expose the heartwood to infection. From these points of 
infection the fungus spreads through the heartwood both upwards and 



EXTERIOR DEFECTS 



113 





downwards. The form which it takes depends upon the species of 
fungus, and of trees attacked. The unsound portion is surrounded by 
a stained portion which is yet sound. The area of the rot increases 
with age of tree and time elapsing since the infection took place. 

In deducting for rot, the amount of the loss depends upon the location 
of the point of infection, usually a rotten knot. Stain which shows at 
one end of a log requires no deduction if the rot of which it is an evidence 
lies in the adjoining log as cut from the bole. On the other hand, two 
or more rotten knots in a log, with stain showing, means a heavy dis- 
count and a possible cull. Sawyers are accustomed to leave such logs 
in the woods and even in the tree without sawing them. Rot from a 
single point of infection will extend 
from 2 feet to as much as 10 or 15 
feet in either du'ection. It is deepest 
and most complete at the point of entry, 
tapering out with increasing distance 
from this point. Rot of this character 
is so irregular that experience is re- 
quired in observing such logs sawed 
before proper deductions can be made 
by scalers. 

In deducting for interior rot, the 
probable extent and shape of the un- 
sound portion therefore depends upon 
the appearance of the ends taken in 
connection with unsound knots. The 
only portions of the log which can be 
scaled are those which will produce 
sound boards having the minimum 

length and width prescribed in the rules for scaling. The deduction 
will take the form of a per cent of the sound scale. Diagrams are some- 
times of assistance, but in logs containing rotten knots the extent of 
rot is usually greater than revealed at the cross section. The appa- 
rent cull must ordinarily be increased, from 25 to 100 per cent. 
Since deduction of length is equivalent to a percentage reduction of 
scale, this method is frequently used. 

Peck in cypress, and the rot found in Incense cedar gives no 
external indications, and is not always revealed on the cut ends of logs. 
This condition tends to the substitution of a straight percentage deduc- 
tion from the total scale instead of reducing the scale of individual 
logs for defects. 

92. Exterior Defects. Exterior defects, on the sides of logs, include 
unsound sap, surface checks, cat faces, fire scars, and scars caused by 



Fig. 19. — Log A is infected at 
the point X and is a cull. At 
the lower end no rot shows, 
but stain only. This stain 
therefore shows at the upper 
end of log B, but causes no 
deduction for cull. 



114 



THE SCALING OF DEFECTIVE LOGS 



mechanical injuries such as hghtning or faUing timber. Irregular 
butt rot, appearing as a small patch on one side, or rot from knots 
which is local in extent, can sometimes be scaled by the methods used 
to scale side defects. 

Exterior defects, especially at the butts of logs, may fall entirely 
outside the inscribed circle representing the top or scaling diameter, in 
which case they cause no deduction in scale. With defects which 

penetrate deeper a further 
portion is included in the 
slab allowed in sawing, 
within this circle. 

Where the defect ex- 
tends but a few feet in 
length, as for instance a 
fire scar at the butt of a 
log, the deduction is con- 
fined to that portion of the 
length of the small cylinder 
whose contents is scaled, 
which is affected by the 
defect. The amount to 
subtract may be found in 
one of two ways; by dia- 
gram of the slab affected by 
the defect, or by culling a 
per cent of the volume of 
the log. 

Deductions by Slabs. 
The dimensions of the por- 
tion to be deducted as a 
slab are not those of the 
piece actually slabbed from 
the butt, but only the depth of the portion lying within the inscribed 
circle of the small end of log. From this again there is subtracted an 
additional amount for slabbing, shown in Fig. 20. The remaining 
depth, multiphed by the average width of the inscribed slab, gives 
the area of the cross-section whose length will be that of the defect, 

, , a-b-l 

and volume, —,-7^. 
15 

In the above figure, the fire scar on the butt log Is 8 inches deep, but only 
5 inches of this is within the inscribed scaling dimensions. Of this Ij inches is 
slab, giving 3j inches for lumber. The widths of the boards lost are 10 inches, 
14 inches and 18 inches. The average width of the rectangle is 14 inches. A 




Fig. 20. — Effect of fire scar at butt, on deduc- 
tions from scale. 





EXTERIOR DEFECTS 115 

diagram measuring 4 by 14 inches, whose length equals that of the fire scar lying 
within the inscribed cylinder, gives the deductions. As the scar gets shallower, 
the length lying within this cylinder is less than its total length. Tables could 
be worked up by a scaler to express the board-foot contents that could be cut out 
of slubs of given thickness on circles (inscribed) of given diameter for a standard 
length of log, allowing a minimum width of board equivalent to that used by the 
log rule (§ 67) But ocular methods are almost equally efficient after practice. 

Deduction by Sectors. Side defects extending deeply into the log 
(Fig. 21) cannot be slabbed off and are not easy to express by diagrams. 
By enclosing them in V-shaped 
areas representing sectors of a 
circle, an idea may be obtained 
of their extent. This method 
may be used for any defect 
occurring wholly on one side 
of the geometric center of a 
log and which is more accu- Fig. 21.— Method of deducting from scale 
rately enclosed by a sector by means of sectors enclosing defective 

than a slab. P°^*'°" «f log- 

The cull per cent for the portion of the log affected is roughly equal to the 
ratio between the area of the circle and of the sector. This rule is exact for the 
ratio 5, and nearly so for smaller or larger sectors. The error in applying the rule 
will average less than 3 per cent of the volume of the log, and if the defect is con- 
fined to a short length, this error is proportionately less for the whole log (from inves- 
tigations of H. D. Tiemann); e.g., a sector equaling one-fourth of a circle calls 
for 25 per cent cull. Cull tables may be made for this deduction, but it is equally 
convenient to apply the percentage directly to the scale. This latter method 
adjusts the cull factor to any log rule (§ 89). 

Other Surface Defects. Stained sap is scaled as sound. When 
unsound or decayed, the scaling diameter is taken inside the sap. 
Surface checks caused by prolonged weathering as in the case of dead 
timber, or by neglect or exposure of logs, must be scaled out in the same 
manner as sap. Cat faces, as defined for cedar poles in the Lake States, 
are defects on the sides of logs caused by some mechanical injury to 
the bark which has caused a wound. A cat face may be accompanied 
by rot, or be merely a dry face, not healed over and forming an indenta- 
tion in the bole. According to its shape and depth, a cat face is deducted 
either as a slab or a segment, of proper length. The term cat face is 
also applied to a fire scar at the butt of a tree, usually partly healed 
over, which may be sound, rotten or wormy. Any surface defect partly 
healed over, on the bole, caused by either fire or mechanical injury, 
whether at the butt or on the bole, may properly be called a cat face. 
Lightning scars, even when the tree is not shattered or killed, usually 



116 



THE SCALING OF DEFECTIVE LOGS 



form a dead streak causing a surface defect, sometimes of considerable 
proportions. 

Breakage. The deduction for splits and breakage caused by felling 
is made either by slabbing or by shortening the log length, to remove 
the portion ruined by the breakage. Where this waste is avoidable, 
owners stipulate that it shall be scaled as sound, but purchasers of logs 
insist on the deduction. In the Pacific Coast States, breakage may 
exceed 25 per cent of the scale. 

93, Crook or Sweep. Crook may be defined as a rather abrupt 
bend in the log at a given point, while sweep is a more gradual bend 
extending over a considerable length. Crooks occurring near the ends 
of a log may be allowed for in scaling by shortening the scaling length. 
With gradual sweep affecting the form of the log as a whole, a different 
deduction is necessary. The effect of sweep or crook upon the scaled 
contents of the log (§ 52) depends directly upon the minunum length 
of boards utilized and scaled, or upon the acceptance of fixed minimum 
scaling lengths for the logs. If it is assumed that the minimum board 
governs the scale, deductions for crook or sweep will seldom be made, 
since almost complete utilization can be obtained of sound crooked 
logs by the box factory. But if the scale of a log is based on the output 
of boards of the standard scaling lengths into which the logs are cut, 
and short lengths cannot be utilized, crook or sweep will cause deduc- 
tions in scale when it exceeds the normal minimum permitted. 

When logs crook in but one plane, the loss in sawed lumber is proportional 
to the relation which the total deflection or crook bears to the diameter of the log, 
and does not depend on the number of inches of crook independent of size of log; 
e.g., for a 12-inch log a 6-inch crook is 50 per cent of the diameter but for a 24-inch 
log, a 6-inch crook is but 25 per cent of the diameter, and a 50 per cent crook 
indicates a crook of 12 inches. 

By diagram checks, and sawing, the per cent of waste due to sweep for a given 
total number of inches of crook per log is found to be independent of the length 
of log, and to show the following results: 

TABLE XVIII 
Deductions for Crook and Sweep 



Sweep in terms of 

diameter of log. 

Per cent 


Waste in terms of 
scale of log. 
Scribner rule 


8i (or -h) 
16§ (or \) 
25 (or \) 
50 (or i) 


Hi 

22 1 
33^ 
66f 



CHECK-SCALING 



ir 



From these results a rule of thumb may be suggested as follows: Add one-third 
to the per cent of sweep as expressed in terms of diameter of log to obtain the 
per cent of cull; e.g., a log 16 feet long and 16 inches in diameter scales 159 board 
feet. With a sweep of 4 inches or 25 per cent, deduct ^X 25 =385 per cent or 
53 board feet; scale, 106 board feet. With a sweep of 8 inches, deduct Ax50 = 66f 
per cent, or 106 board feet; scale 53 board feet. With a sweep of 2 inches no 
deduction would be made, since this is merely the normal crook. 

Logs which crook in two or more planes must be culled far more heavily than 
when the axis hes in a single plane. For a given per cent of crook the scale is 
roughly proportional to the square of the per cent scaled by the deductions set 
forth above; e.g., a log which scales 50 per cent or one-half if crooked in one plane 
will, if crooked in two planes, scale {^)^ or 25 per cent of its contents. 

94. Check-scaling. By check-scaling is meant the re-scaling of 
selected logs or of a portion of a total run of logs, in order to determine 
the relative accuracy of the original scale, check the methods used by 
the scaler and detect and correct errors in these methods. A re-scale 
requires the remeasurement of all of the logs. The necessity for a 
re-scale is usually revealed by a check-scale. 

Where a number of scalers are employed, check scaling becomes 
necessary in order to maintain uniformity in scaling practice. No 
matter how carefully the standard of scaling practice is set forth in 
printed instructions which cover not only the " scale " with respect 
to diameters, length, taper and trimming allowance, but rules for deduc- 
tions for defects, individual scalers tend to vary from this standard 
through habit or carelessness and inexperienced men are slow to acquire 
accuracy, especially in scaling defective logs. 

A check scale should be made by the most experienced man available as fre- 
quently as possible, but usually at from three to sbc months' intervals. Where 
logs are numbered, the original scale should show the deductions made from the 
full scale of each log (§ 85). The check scale can be made at random on as many 
logs as there is time for. The total scale for the logs checked is then compared 
with the original scale of the identical logs, keeping separate the sound and the 
defective logs. Using the check scale as 100 per cent, the per cent of error in 
scaling is computed according to the following plan: 



Sound logs 



Scale by 



No. of logs 



Scale per cent 
+ or — 



Defective logs 



No. of logs 



Scale per cent 
+ or — 



Total 



No. of 
logs 



Scale per cent 
+ or — 



James Smith 
Cheek scale by 
John Kipp 



The standard of accuracy in the U. S. Forest Service for check scaling requires 



118 THE SCALING OF DEFECTIVE LOGS 

that the scale should not vary from the check scale by more than the following 
pfer cents: 

For sound logs, within 1 per cent; 
For logs up to 10 per cent defective, within 2 per Cent; 
On logs 11 to 20 per cent defective, within 3 per cent; 
On logs over 20 per cent defective, within 5 per cent. 

Check scales are made usually for the purpose of correcting the scaler, but not 
as a basis of altering the scale. Only where the original scale is shown to be 
decidedly in error so as to work an injustice on the purchaser (or seller) are logs 
ever re-scaled. 

Personnel. Scalers should never be reprimanded in general terms for scaling 
too close or too high. The result is usually a worse error in the opposite direction. 
Instead, the scale should be checked by individual logs to discover the sources of 
error and the scaling practice corrected in detail. The fault may lie in some 
specific practice such as an erroneous method of obtaining diameters or in allowing 
for certain common defects. 

Mill-scale studies do not furnish an adequate or satisfactory check 
on scaling, but serve merely to determine the over-run. The scale, 
if in error, must be corrected by re-scaling the logs, not by measuring 
the lumber (§ 74). Such studies do furnish an indication of the scale 
of defective logs, where the scaler's judgment may be in error, but an 
exact check is impossible, as it would require the rejection of boards 
sawed from the taper, which is not practicable. 

95. Scaling from the Stump. Where timber has been cut in tres- 
pass and the logs removed, the evidence remaining is the stump, the 
indentation on the ground where the butt struck in falling, the sawdust 
where the cuts were made in sawing into log lengths, and the top, 
giving the upper diameter. The length of the tree can then be meas- 
ured, and occasionally, that of each log sawed. The total difference 
in diameter between top and butt is distributed according to the accepted 
local customs for scaling long logs. This gives the scaling diameter 
and length of each log in the tree. Specifi.c deduction for defect can 
be made only for stump rot, since this is revealed by the stump and 
the average deduction for rot having the character and extent of that 
shown can be made from the butt log. Further deductions if made 
must be based on the average per cent of cull for timber of the given 
species and character. 

When tops are removed, burned or otherwise rendered indistinguish- 
able, neither the top diameter nor the length of the tree can be judged. 
Merchantable length must then be based upon the heights of trees in 
the vicinity, and volumes taken from volume tables (§ 121) for trees 
of given diameter and height. A table of stump tapers (§ 168) must 
be used to express the diameter of the stump in terms of diameter 4| 
feet from ground (§ 134). 



THE SCALER 119 

96. The Scaler. A scaler with no other duties can number and scale 500 logs 
per day, running 10 logs per 1000 board feet or 50,000 board feet at a cost of about 
10 cents per 1000 board feet, based on wages and subsistence of $125.00 per month. 
This average can be exceeded but is apt to be reduced in quaotity by time lost in 
travel to and from the logs, scaling in the woods, or an insufficient number of logs 
on hand* daily to occupy the full time of the scaler. Often these logs must be 
scaled daily and cannot accumulate, because of insufficient room on the skids, 
thus keeping a scaler in constant attendance. A scaler thus employed is often 
given other duties such as inspecting the work of the saw crews. National Forest 
Scalers supervise the disposal of brush, closeness of utilization and the marking 
of timber for felling. This reduces the average cost of scaling to approximately 
the basis mentioned. 

Commercial scaling by private companies is done far more rapidly and cheaply 
because of the elimination of numbering, and by careless or indifferent methods 
of measuring lengths and deducting for defects. A scale of 1000 to 1500 pieces, 
and 100,000 board feet per day and a cost of 5 cents per 1000 board feet or less 
is not unusual on large operations. 

So important is an accurate scale that the scaler must be given every facility 
to obtain the measurement with the least trouble and greatest certainty. This 
usually means providing a sufficient force of scalers so that the}'^ may be on hand 
at the most favorable time, or constantly. When on account of small or scattered 
operations the logs must accumulate the scaler is handicapped in various ways. 
Large and high rollways require two men, one on each side, to get the length, even 
approximately, and to distinguish top from butt, of each log. Logs landed on ice 
will in time by their weight cause cracks and flooding, and small logs are frozen in. 
Whole rollways may break through the ice and become partially submerged. 
Snow covers and buries the piles, and logs are overlooked. Logs may be rolled 
down steep banks and lie in such confusion that scaling is difficult and dangerous. 
Steam skidders pile logs in huge heaps impossible to scale at all until loaded on 
cars. The inability of the scaler to cover his route at frequent intervals encourages 
careless sawing, timber stealing and poor scaling. Contracts should specify that 
logs must be piled or skidded in such a manner that accurate scaling is possible. 

Legal Status of Scaler. "A scaler whose services are agreed upon by both parties 
to a contract or sale, is the sole arbiter between these parties in determining the 
amount of the scale. But if one party furnishes the scaler without the expressed 
consent or agreement of the other, his scale may be appealed from." Frisco 
Lumber Co. vs. Hodge, U. S. Circuit Court of Appeals, 218 Fed. Rep. 778. 

"A scaler furnished by the defendant and boarded by plaintiff would be one 
mutually agreed upon, and they must abide by his decisions." Connecticut Valley 
Lumber Co. vs. Stone, U. S. Circuit Court of Appeals, 212 Fed. Rep. 713. 

"Binding in the absence of fraud or mathematical mistakes." Hutchins vs. 
Merrill, Supreme Court Maine, 84 Atlantic 412. 

"Scale made by scaler appointed by defendant not binding in absence of some 
stipulation to that effect in contract." Owen vs. J. Neils Lumber Co., Supreme 
Court of Minnesota, 145 Northwestern 402 (1914). 

"Scaler who performed his duty fairly and honestly, though negUgently, could- 
not be held liable for discrepancy between the amount he scaled and the amount 
of logs delivered, as permitting such action would destroy independence of arbitra- 
tion." Hutchins vs. Merrill, Supreme Court Maine, 84 Atlantic 412. 



120 THE SCALING OF DEFECTIVE LOGS 



References 

Instructions for the Scaling and Measurement of National Forest Timber, U. S. 

Dept. Agr., Forest Service, 1916. 
Checking Check Scalers, T. S. Woolsey, Jr., Proc. Soc. Am. Foresters, Vol. XI, 

1916, p. 245. 
Methods of Scaling Logs, Henry S. Graves, Forestry Quarterly, Vol. Ill, 1905, 

p. 245. Cull tables by Tiemann. 
Methods of Making Discounts for Defects in Scaling Logs, H. D. Tiemann, Forestry 

Quarterly, Vol. Ill, 1905, p. 354. 



CHAPTER IX 
STACKED OR CORD MEASURE 

97. Stacked Measure as a Substitute for Cubic Measure, Stacked 
or cord measure is the cubic space occupied by stacked wood when 
the exterior dimensions of the stacks are measured. This is expressed 
in terms of standard units termed cords. Wood in the form of round 
bolts or spht bolts, which are termed billets (§9) is usually intended 
either for use as bulk products such as firewood, pulpwood or acid wood, 
or for manufactured articles whose dimensions conform to those of 
the bolts or billets. 

For the former uses, the total cubic contents of the wood, or of wood 
and bark, is desired. This could be obtained as with logs, by measuring 
the dimensions of each separate bolt and totaling their contents. On 
account of the smaller sizes, greater number, and irregularity of form, 
especially of billets, such a method would be time consuming, inaccu- 
rate and impossible to check as to results without complete measure- 
ment. Yet it is quite extensively employed to obtain actual cubic 
contents of logs and bolts for commercial purposes, when the material 
is fairly large and of regular shape (§ 29). 

Where the pieces are short, small, split, or irregular in form, the 
more convenient and simple method is to stack the wood in ranks and 
measure the surface dimensions to get stacked cubic contents including 
both solid wood and air space. 

98. The Standard Cord versus Short Cords and Long Cords. A 
standard stacked cord is a pile, 4 feet high, 8 feet long, of pieces 4 
feet long, and contains 128 stacked cubic feet. For bulk products, the 
net cubic contents of wood, either with or without bark is desired. The 
use of wood with bark for fuel for domestic purposes utilizes by far the 
greater portion of all wood sold in bulk. For this purpose the stand- 
ard cord is the basis of delivery in the rough, to wood dealers. 

But the domestic consumer seldom burns 4-foot wood, and usually 
requires short wood of varying sizes commonly between 12 and 24 
inches in length and making 4, 3 or 2 cuts to a 4-foot stick. Other 
special lengths may be specified when the wood is cut direct from the 
tree. This demand gives rise to the short cord. A short cord is a pile 
measuring 4 by 8 feet on the side or face and one rank deep. The depth 
and cubic contents depends on the length of the pieces. Since this 

121 



122 STACKED OR CORD MEASURE 

substitution of surface measure reduces the cubic volume of short 
cords, either the price must be reduced, or the full cubic contents of 
a standard cord secured by requiring the cord to be two, three or four 
ranks deep, or to have an additional length sufficient to make up 128 
stacked cubic feet. A standard cord of 4-foot wood when cut into 
stove lengths is considered a full cord, although in repiling it shrinks 
from 8 to 13 per cent in stacked volume (§ 108). When the cord of 
short wood is measured on this basis, the full dimensions of a standard 
cord cannot be required on repiling. 

Wood is also cut longer than 4 feet. The term lo7ig cord usually 
refers to a cord 4 by 8 feet in surface bj" 5 feet in depth and containing 
160 cubic feet. The standard length of stick for hardwoods for dis- 
tillation or acid wood is 50 inches, giving a cubic contents of 133| 
cubic feet. Unless long cords are accepted by custom, stacks measur- 
ing more than 4 feet in length of stack are reduced to their equivalent 
volume in standard cords. When pulp wood bolts, ordinarily cut 4 
feet long, are cut 8, 12 or 16 feet long, they are measured as standard 
cords, a stack 4 by 8 by 8 feet containing 2 cords. 

99. Measurement of Stacked Wood Cut for Special Purposes. Stacked cubic 
measure is commonly employed in measuring bolts or split billets intended for man- 
ufacture into spokes, handles, staves for slack and tight cooperage, shingles and 
similar piece products. Bolts measuring over 12 inches in diameter are usually 
scaled in board feet. Billets, if spUt or rived into pieces each of which is to be 
shaped into one finished article such a spUt staves, may be counted. 

Bolts intended for sawing are usually measured by stacked contents. The 
lengths of the bolts sawed from the tree must correspond to the required length 
of the product plus a small margin for trimming, or must be a multiple of this 
length, to avoid waste. For spokes, 30 inches is a common length. Handles 
require lengths of from 12 to 60 inches. Common lengths for staves for tight 
cooperage are 19 inches and 38 inches. The demands of the market or purchaser 
determine the length in every case. 

The measurement of shingle bolts is frequently by double cords, in lengths of 
8 feet. On the West Coast, the bolts are cut in lengths equal to 3 shingles. For 
16-inch shingles the cord is 4 feet 4 inches in depth, while for 18-inch shingles, 
the length of bolt required is 4 feet 8 or 10 inches. Shingle bolts illustrate the 
tendency to simplify and standardize measurements of products to save expense. 
The bolts are not uniform in size, and one cord may contain from 16 to 40 bolts. 
But it is common practice to first determine the average number of bolts in a cord, 
and then measure the remainder by counting the bolts to avoid stacking. The 
number agreed upon is used as a divisor to obtain the quantity in cords. 

Stacks measuring more or less than 4 feet in length of stick can thus be measured 
in either of the two ways described above (§ 98). Surface feet or 32 square feet 
equivalent to 4 by 8 feet may be taken as a short cord. But stacked contents 
based on the standard cord of 128 cubic feet is just as commonly employed. For 
instance, in cooperage it is a common custom to measure 36-inch stave bolts in 
ranks 4 by 11 feet for one cord, giving 132 cubic feet or approximately a standard 
cord. 



EFFECT OF SEASONING ON VOLUME OF STACKED WOOD 123 

100. Effect of Seasoning on Volume of Stacked Wood. Green 
hardwoods shrink on seasoning, decreasing from 9 to 14 per cent in 
volume. Conifers shrink from 9 to 10 per cent. Contractors some- 
times 4stipulate an extra height of 3 to 4 inches on the stack to offset 
this loss. Where such extra allowance for shrinkage, or for any other 
reason, is required, it must be specified by contract unless generally 
accepted in the locality. 

101. Methods of Measurement of Cordwood. Stacked cord wood 
is measured by a stick usually 8 feet long, marked off in feet and tenths. 
Choppers prefer to pile each cord separately, since the division into 
a number of smaller piles reduces the cubic contents required for one 
cord (§ 103). When surface measure, 32 square feet, is accepted for 
short or long cords, their measurement is identical with that of standard 
cords, the length of piece being measured only to insure conformity 
with specifications. Stacks piled to more or less than standard height 
and length are reduced to cords by dividing the surface feet by 32; 
e.g., a stack measuring 12.7 feet by 6.4 feet contains 81.28 surface feet, 
or 2.54 cords. 

When standard stacked contents is used as a basis, the length of 

piece is also measured, the cubic contents of stacked wood obtained 

and divided by 128; e.g., a stack of 30-inch bolts with the above surface 

203 2 
dimensions gives 81.28 by 2.5 = 203.2 stacked cubic feet; — -^ = 1.5875 

128 

standard cords, while a similar stack of 5-foot wood gives 81.28 by 5 

406 4 
= 406.4 stacked cubic feet. ' =3.175 standard cords, instead of 

128 

the 2.54 cords based on surface standard. 

A cord foot is a pile measuring 1 by 4 by 4 feet or containing one- 
eighth of a standard cord. It is also termed a foot of cordwood, being 
equal to 1 foot in length in a stack of cordwood of standard dimensions. 
The unit applies to short or long cords when surface only is measured 
and not cubic contents. 

The chopper is required to pile the rank to an even height, pref- 
erably the standard of 4 feet. Unless otherwise specified, the height 
of the pile is to be the average height of the tops of the sticks in the top 
layer. With uneven, crooked or poorly piled stacks a point 1 or 2 
inches below this is taken. From this height is subtracted whatever 
allowance is required for shrinkage, when so specified. 

If the ends of the stacks are not vertical the length is measured at 
one-half the height of the pile. If wood is piled in irregular stacks 
the average of both height and length is obtained, if necessary from 
several equally spaced measurements. 

Wood piled on inclined surfaces is measured incorrectly if the length 



124 



STACKED OR CORD MEASURE 



of the pile is taken parallel with the surface of the ground or top of 
stack, while height is taken vertically. The true contents of a stack 
with the dimensions shown in Fig. 22 is 87.5 per cent of a cord. The 

correct measurement is secured if 
' *^"" length and height are taken at 

right angles whether or not the 
length is taken horizontally or 
along the surface. 

102. Solid Cubic Contents of 
Stacked Wood. The stacked cord 
is a measure piu'ely of convenience. 
The purchaser is interested not in 
the cord, but in its solid cubic 
contents of wood. Stacked round 
bolts can never give 128 cubic feet 
of wood to a cord. The highest 
possible contents would be ob- 
tained from bolts which were per- 
fectly cylindrical and of uniform 
diameter. These, if stacked in 
hexagonal formation, or alternat- 
ing, and with one end bolt in each 
tier split in half to fill out the tier, would give 116.07 cubic feet, or 
90.68 per cent of 128 cubic feet, which is the relation of the area of an 
inscribed circle to that of a hexagon. This relation holds true for bolts 
of any length or diameter. 




Fig. 22. — In the example given, the ver- 
tical height of the pile must be 4.57 
feet to give 128 cubic feet. The actual 
pile measures 112 cubic feet by either 
method. 





Fig. 23. — Hexagonal piling — 116.07 cubic feet per cord or 90.68 per cent solid wood. 
Square piling — 100.5.3 cubic feet per cord or 78. .54 per cent solid wood. It 
is evident that neither the diameter nor the length of sticks would in any 
way influence the solid cubic contents of a cord unless taken in conjunction 
with some other factor whose effect varies with the dimensions of the piece. 

When these cylinders are pUed directly above one another in square 
formation, the cubic contents of a cord becomes 100.53 cubic feet, or 
78.54 per cent of 128 cubic feet, which is the relation of the area of 
an inscribed circle to that of square. 

103. Effect of Irregular Piling on Solid Contents. In actual prac- 
tice, the solid contents of a cord seldom exceeds 1 00 cul^ic feet. Straight 



EFFECT OF IRREGULAR PILING ON SOLID CONTENTS 125 

smooth sticks of uniform sizes, carefully piled, may yield from 105 
to 107 cubic feet, but never as much as the 116 cubic feet theoretically 
possible. This loss is due first to irregular piling, and second, to vari- 
ation* of the bolts or sticks from uniform cylindrical form. 

Piling exercises an enormous influence, which increases in direct 
proportion to the irregularities of form. When to extreme crooked- 
ness and surface irregularities is added dishonest piling, including the 
laying of sticks at angles with each other, or even piling over stumps 
and other trade practices, the purchaser may incur a loss of from 20 
to 30 per cent from piling alone. Choppers are always paid by stacked 
measure and close supervision is required to secure a full cord. The 
factor of piling may cause more variation in the solid contents of a cord 
than that of form of sticks. Since this factor depends upon the laborer, 
the contents of a cord of wood, as a commercial standard, is based on 
what can be expected of choppers rather than a theoretical maximum. 
Conversion factors for obtaining cubic contents of wood are based on 
average conditions of piling. The cord can never be satisfactorily used 
as a basis of scientific measurements of volume produced by trees and 
stands, or of growth, though for convenience, cubic contents is often 
converted into cords to express the results of these investigations. 

104. Effect of Variation in Form of Sticks on Solid Contents. 
Variation in the form of sticks is caused by taper, eccentric cross sections, 
crook, and irregularities or roughness of surface. All departures from 
cylindrical form increase the air space in a stacked cord. 

The effect of taper can be partially overcome by piling bolts with 
large and small ends alternating. But this is never done in practice. 
Sticks split from bolts which include stump taper are apt to be some- 
what curved as well as tapering. Sticks with eccentric cross-sections 
do not pack as closely as round sticks and give a smaller per cent of solid 
contents. 

Crook is one of the most important factors in reducing the cubic 
contents of a cord. The slightest departure from a straight axis exerts 
a corresponding influence in increasing the air space in stacking. Very 
crooked sticks may reduce the contents of a cord by 50 per cent. 

Irregularities of surface in round sticks are caused by bark, knots, 
stubs and swellings. Every such protuberance, by contact with adjoin- 
ing sticks, decreases the solid contents of the stack. Split sticks are 
irregular in both form and surface and always take up more room than 
the round bolts from which they were split or round bolts of equal 
diameter and straightness. 

Since sticks with the smoothest surface and least taper will pack 
the closest, and the removal of bark affects both factors favorably, the 
cubic contents of a cord of peeled wood is always greater than the cubic 



126 STACKED OR CORD MEASURE 

contents of a cord of wood with bark, for the same species and sizes of 
sticks. The shrinkage in stacked contents after peehng exceeds that 
caused by loss of bark because of this closer piling. Bark is a waste 
product for pulpwood or excelsior and purchasers prefer to buy peeled 
wood. 

The thinner the bark on a tree the smoother it is apt to be. Species 
with smooth bark yield appreciably more solid contents in stacks than 
thick-barked trees, because in the latter case the bark is usually irregular 
and fissured. Hence conifers such as spruce and balsam, and hard- 
woods like white birch and poplar give the highest contents per cord, 
while hardwoods such as oak and maple yield considerably less per 
cord than conifers. 

The same difference holds for branch wood as contrasted with body 
wood, open-grown and limby trees compared with those grown free 
from branches in close stands, and split wood with twisted grain com- 
pared to straight grain. 

While the splitting of sticks decreases the solid contents, by increasing 
the irregularities of surface and the effect of crook through reduced 
diameters, split cordwood is usually cut from much larger bolts than 
round sticks, and hence a cord of split wood may contain a greater 
solid content than one of round sticks, especially if the round pieces 
are below 3 inches and cut from limbs. 

105. Effect of Dimensions of Stick on Solid Contents. The effect 
of a given amount or rate of crook, or of given irregularities of surface, 
in diminishing the solid contents of a stack, increases with increased 
length of stick, but this effect is more nearly proportional to the square 
of the length than to the length. Hence the longer the sticks in a 
stacked cord, the less its net cubic contents, other factors being equal. 

This explains the shrinkage in cubic volume when 4-foot wood is 
cut into shorter lengths and restacked. In sticks longer than 6 feet 
this becomes a serious factor and pulpwood from fairly straight logs 
when sold in from 8- to 12-foot lengths gives about 12 per cent less cubic 
contents than for 4-foot bolts (Table XXI, p. 130). 

Conversely, the cubic volume of sticks increases as their cross- 
sectional area, which is as the square of the diameter, while the effect 
of both crook and surface irregularities increases in porportion to the 
surface of the stick, which is directly in proportion to diameter and 
consequently less than cross-sectional area or volume. A crook of 
2 inches in a stick with 3-inch diameter has twice the effect that a 
2-inch crook would have on a 6-inch stick. Due to these relations, the 
solid contents of a cord of wood always increases with the increased 
average diameter of the sticks, but diminishes with increased 
length. 



THE BASIS FOR CORDWOOD CONVERTING FACTORS 



127 



106. The Basis for Cordwood Converting Factors. The value of 
stacke^:! wood depends upon the quantity of wood contained in the 
stacked cord as well as upon its quality. It is just as consistent to 
require a knowledge of the solid cubic contents of stacked cords as it 
is to measure sawlogs for board-foot contents by a log rule. For this 
purpose, converting factors are required, and these factors are deter- 
mined by actual measurement of the solid wood in cords composed of 
sticks of different diameters and degrees of straightness. 

Since a cord contains 128 cubic feet of space, the solid contents in 
cubic feet may be expressed in terms of per cent; e.g., a cord containing 
90 cubic feet of wood gives 70 per cent of stacked contents in wood. 
A cord of theoretically perfect cylindrical sticks piled square gives 
100.5 cubic feet, or 79 per cent (§ 102). This in actual practice is about 
the maximum contents of stacked cord, no matter how the piling is 
done, for losses caused by taper, crook and surface compensate for any 
gain by hexagonal over square arrangement of sticks. Smooth pine 
or white birch may give 102 to 107 cubic feet for large sticks, but the 
attainable maximum solid cubic contents of cords can for commercial 
purposes be set at 100 cubic feet. 



TABLE XIX 
Solid Contents of Stacked Wood * 



Class of product 


Per cent 

solid contents 

in stack 


Cubic feet solid wood 
in one cord or per 
cent of standard 

contents of 100 cubic 
feet per cord 


Large smooth logs or bolts ... 


75-80 
60-75 
50-65 
30-45 
30-40 


96 0-102 4 


Average split firewood 


76 8- 96 


Top and branch wood 


64 0- 83 2 


Fagot material (small branches and twigs) .... 
Stumps and roots 


38.4- 57.6 
28.4- 51 2 







* Adolph R. von Guttenberg, in Lorey's Handbuch der Forstwisscnschaft, Vol. Ill, 1903, 
Chap. XII, p. 179, Tubingen. 

There is thus a choice of two methods of expressing converting 
factors for indicating the solid or cubic contents of wood in a cord; 
first, the number of feet of solid wood in a cord of 128 stacked feet; 
second, the per cent of a stacked cord which this cubic contents repre- 
sents. Of the two, the former is preferable for two reasons; first, it 
is directly applicable to cubic contents of trees as a divisor or con- 
verting factor to obtain cords; second, it indicates the comparative 



128 STACKED OR CORD MEASURE 

solid volume in cords of different cubic contents on a basis which prac- 
tically amounts to a 100 per cent commercial standard. For if 100 
cubic feet, as indicated above, is the practical maximum solid cubic 
contents of a cord of stacked wood, a cord containing 70 solid cubic 
feet bears a 70 per cent relation to this maximum, regardless of the fact 
that 70 feet is but 54 per cent of the space in a stacked cord of 128 feet. 
This accidental relation holds good only for standard cords. To apply 
this same basis of comparison, instead of the per cent of stacked con- 
tents, to long or short cords, the solid contents would have to be com- 
pared to 78.12 per cent or yff of the stacked contents. Average cord- 
wood worked up from hardwoods, either split or round, is often reckoned 
at 90 cubic feet or 90 per cent of a maximum cord, which is 70 per cent 
of stacked contents. 

107. Standard Cordwood Converting Factors. The cubic contents 
of stacked wood has been thoroughly investigated by European author- 
ities on the basis of the stacked cubic meter, of length equal to 39.37 
inches or 8.63 inches short of a 4-foot standard. According to the per 
cents given in Table XXI (p. 130) these results should give about 1 per 
cent more than the contents of similar sticks 4 feet long. 

The following Table XX is adopted from the results of an investi- 
gation conducted by Prof. F. Baur, and published in a pamphlet entitled 
" Untersuchungen iiber die Festgeholt und das Gewicht des Schicht- 
holzes und der Rinde," Augsburg 1879, pp. 97-99. These factors 
may be regarded as standard for 4-foot lengths, after subtracting 1 per 
cent. 

The difference in per cents between hardwoods and conifers in this 
table is seen to fall largely in the smaller sizes. Wliere branch wood 
is mixed in the cord the per cent of difference between hardwood and 
conifers, usually about 6 per cent, may be increased to 12 or 15 per 
cent, since many conifers lack mei'chantable branches, while hardwood 
branches are usually crooked. 

108. Converting Factors for Sticks of Different Lengths. The 
influence of length on per cent of solid contents is fairly constant for 
sticks of all diameters, but differs tremendously according to the amount 
of crook in the average stick. Table XXII gives average results 
for conifers, which as a rule are much straighter than hardwoods. It 
is seen in the table that the per cents when standardized for sticks of 
the same diameter do not differ much, whether the sticks average over 
5.5 inches or are between 1 inch and 2.5 inches in diameter. 

The differences in contents caused by crook and surface irregularities is well 
shown in Table XXIII, prepared for hardwoods by Konig, p. 131. In this table 
the values for straight sticks 4 feet long slightly exceed the values in Table 
XXI since these sticks are selected. But for other lengths even in this class the 



CONVERTING FACTORS STICKS OF DIFFERENT LENGTHS 129 



percentages increase more rapidly than for conifers; while for crooked and knotty 
sticks the differences caused by length are excessive, when added to those caused 
by diameter. 

TABLE XX 
Standard Converting Factors for Cordwood 













Cubic feet 












solid wood in 










Per cent 


a cord or 


Species 


Diam- 
eter 


Class of 
material 


Character of 
piece 


solid wood 
in a 
cord 


per cent of 

standard 

contents of 

100 cubic feet 












per cord 


Conifers 


Large 


Round logs 


Straight 


80 


102.4 




Medium 


Split firewood 


Straight, smooth 


75 


96.0 




Medium 


Split firewood 


Crooked, knotty 


70 


89.6 




Small 


Firewood 


Round bolts 


70 


89.6 




Small 


Firewood 


Top wood 


60 


76.8 




Small 


Strips 


Hewn from bole 


50 


64.0 




Small 


Chips 


Hewn from bole 


45 


57.6 


Hardwoods 


Large 


Sawlogs 


Straight 


80 


102.4 




Medium 


Split firewood 


Straight, smooth 


70 


89.6 




Large 


Split firewood 


Knotty, crooked 


65 


83.2 




Small 


Firewood 


Round bolts 


65 


83.2 




Small 


Firewood 


Knotty, crooked 


55 


70.4 




Small 


Firewood 


Top wood 


55 


70.4 




Small 


Firewood 


Branch wood 


45 


57.6 




Small 


Strips 


Hewn from bole 


35 


44.8 




Small 


Chips 


Hewn from bole 


25 


32.0 




Small 


Brush 


Long branches 


15 


19.2 



109. Converting Factors for Sticks of Different Diameters. The 

figures in table XXIV indicate the influence of diameter of stick upon 
solid contents of stacked cords, for various species. The differences in 
contents for species is due entirely to differences in form and smooth- 
ness of sticks. 

Second-growth white pine and Norway or red pine give results approximating 
white birch. Old growth, knotty twisted grain and limby northern hardwoods 
give 60 cubic feet per cord, as against 90 cubic feet for tall slender straight clear 
second-growth. A cord of average hardwoods does not contain more than 70 
cubic feet. A cord of second-growth hickory spoke bolts contains 95 cubic feet. 
Chestnut acid wood on the Pisgah National Forest, N. C, is scaled as 110 cubic 
feet of wood per cord of 160 stacked cubic feet, or 87 cubic feet per standard 
cord. In California, a cord of red and white fir, averaging 60 sticks, contains 81 
cubic feet. Western juniper in Arizona averages 62 cubic feet of solid wood 
per cord. 



130 



STACKED OR CORD MEASURE 



TABLE XXI 

Conifers * 
Influence of Length of Stick upon the Solid Cubic Contents of a Cord 





SoUd contents 




Solid contents 




SoUd contents 




Length 
of 

stick. 


per cord. 

Sticks over 

5.5 inches in 

diameter at 

small end. 


Per cent 

in terms 

of 4-foot 

sticks 


per cord. 

Sticks from 2.5 

to 5.5 inches in 

diameter at 

small end. 


Per cent 

in terms 

of 4-foot 

sticks 


per cord. 

Sticks from 1 

to 2.5 inches in 

diameter at 

small end. 


Per cent 

in terms 

of 4-foot 

sticks 


Feet 


Cubic feet 




Cubic feet 




Cubic feet 




1 


91.80 


+ 3.2 


85.25 


+ 3.4 


65.69 


+ 3.2 


2 


90.90 


+ 2.2 


84.35 


+ 2.3 


65.32 


+ 2.7 


3 


89.98 


+ 1.2 


83.40 


+ 1.6 


64.60 


+ 1.5 


4 


88.92 





82.42 





63.62 





5 


87.75 


- 1.3 


81.30 


- 1.3 


62.60 


- 1.6 


6 


86.45 


- 2.8 


80.00 


- 3.0 


61.60 


- 3.2 


8 


83 . 75 


- 5.8 


77.20 


- 6.3 


59.40 


- 6.6 


10 


81.00 


- 8.9 


74.30 


- 9.9 


56 90 


-10.5 


12 


78.05 


-12.2 


71.20 


-13.6 


54.25 


-14.7 


14 


74.85 


-15.8 


67.95 


-17.5 


51.50 


-19.0 



* Raphael Zon, Forestry Quarterly, Vol I, 1903, p. 132. 

These results were verified by test on balsam fir in the Adirondack region of New 
York 

TABLE XXII 

Influence of Length of Stick on Solid Cubic Contents of a Standard Cord, 

Balsam Fir 







Volume 




Length. 

Feet 


Diameter of sticks, 
small end, 7 inches 

and over. 

Cubic feet 


Loss in long 
sticks. 

Per cent 


Diameter of sticks, 
small end, 4 to 7 
inches. 
Cubic feet 


Loss in long 
sticks. 

Per cent 


4 

8 

12 

16 


96.7 
91.6 
86.2 
80.2 


- 5.3 
-10.8 
-17.1 


92.4 
87.4 
81.6 
75.5 


- 5.4 
-11.6 
-18.3 



This table was based on 56 cords by R. Zon, Bui. 55, U. S. Dept. of Agriculture, 
p. 52. 



CONVERTING FACTORS STICKS OF DIFFERENT DIAMETERS 131 

TABLE XXIII 

Interdependence of the Stick Length and the Volume of Solid Wood per 

Cord * 



Length 


Straight Sticks 


Crooked Sticks 


Knotty Sticks 


of 














stick. 
















Volume. 


Difference. 


Volume. 


Difference. 


Volume. 


Difference. 


Feet 


Cubic feet 


Per cent 


Cubic feet 


Per cent 


Cubic feet 


Per cent 


1 


99.81 


+8.3 


93.47 


+ 14.1 


89.60 


+20.7 


2 


97.28 


+5.5 


89.60 


+ 9.4 


84.48 


+ 13.8 


3 


94.72 


+2.8 


85.76 


+ 4.7 


79.36 


+ 6.9 


4 


92.16 


0.0 


81.92 


0.0 


74.24 


0.0 


5 


89.60 


-2.8 


78.08 


- 4.7 


69.12 


- 6.9 


6 


87.04 


-5.5 


74.24 


- 9.4 


64.00 


-13.8 



* Cited in Dr. Miiller's Lehrbuch der Holzmesskunde, Graves Mensuration, p. 104. 



TABLE XXIV 

Solid Contents of a Standard Cord Based on Diameter of Stick 
Average, 4-foot wood 



Average 










Mixed 


diameter at 
middle 


Paper B: 
birch.* 


ilsam ^ . . 
„ , Spruce.; As 


pen.§ Be 


, J Red 
ech.§ , ,, 
maple. II 


hard- 
woods. § 


of sticks. 












Inches 


Cu. ft. C 


u. ft. Cu. ft. C 


u. ft. C 


u. ft. Cu. ft. 


Cu. ft. 


3 


64 


76 75 


49 


67 


60 


4 


72 


82 80 


57 


69 


65 


5 


82 


86 84 


64 


54 70 


69 


6 


87 


88 86 


71 


62 72 


73 


7 


91 


90 88 


77 


70 74 


77 


8 


96 


91 90 


83 


77 77 


80 


9 


100 


92 91 


88 


83 80 


83 


10 


103 


93 92 


92 


88 84 


85 


11 


105 


94 92 


96 


93 87 


88 


12 


105 


93 




90 


90 


13 


105 


94 




92 


92 


14 




95 




93 


95 


15 




96 




95 


97 


16 




96 




96 


99 


17 




97 




96 




18 




97 









* S. T. Dana. 



t R. Zon. 



t H. L. Churchill. 
E. E. Carter. 



§ E. H. Frothingham. 



132 STACKED OR CORD MEASURE 

110. The Measurement of Solid Contents of Stacked Cords — 
Xylometers. The solid or cubic contents of stacked cords must be 
actually measured in order to determine the converting factors for 
wood as influenced by any of the above conditions. The purpose may 
be to obtain either an average factor for commercial use, or to further 
test the effect of crook, diameter or length of sticks speciall}- selected. 

Two methods of measurement are available, actual calipering or 
stereometric ' calculation, and xylometric - measurement. By the first 
method, the diameter of each bolt is measured in the middle (Ruber's 
method) taking two measurements at right angles to obtain the average. 
The length is measured if necessary, but the sticks arc usually cut to 
a standard length. Split billets cannot be measured by this means, 
and in this case, the round bolt must first be measured l)efore splitting. 
The measured wood is piled and the contents of the sticks required to 
make a stacked cord are totaled for as many cords as possible, to obtain 
average factors. 

Wood after splitting, or very small crooked or irregular pieces such 
as branches or root wood, is best measured by a xylometer.^ The dis- 
placement of water when wood is submerged in a tank is' exactly equal 
to the cubic volume of the wood. The only question is the fo m of the 
tank and method of measuring the cubic volume of water displaced. 

One plan (invented by Karl Heyer, Giessen, 1846) is to have an 
overflow spout flush with the water level and to catch and measure 
water which overflows. 

But this is found to take seven times as long as Reisig's method 
(Darmstadt, 1837) which employes a tank about 5| feet high and about 
twice as wide as the diameters of the largest sticks. The cross-section 
must be uniform at all points. The scale is worked out for cubic feet 
and decimals, corresponding to the inch scale in height of water in the 
tank and is either marked on the inside of the tank, or better on a stand 
pipe of glass outside the tank, with proper connection, and carefully 
plumbed. This gives instant readings when a piece is submerged. 
The endwise position favors complete submersion. 

111. Cordwood Log Rules. TheHumphrey Caliper Rule, 1882. Cord- 
wood log rules are in use in Southern New Hampshire and in Massa- 
chusetts for measuring the cubic contents of white pine logs in terms 
of stacked cords and stacked cubic feet. These rules are based upon 
the principle of the circle inscribed in a square (§ 102). It is assumed 
that a cord, no matter what the diameter, length or character of the 
timber, contains 100.5 cubic feet of solid wood. The diameter is cali- 
pered in the middle of the log outside the bark, but the rule could be 

^Stereometry, the art of measuring solid bodies. Stereos (Gr.)= solid. 
^Xylos (Gr.)=water. 



DISCOUNTING FOR DEFECT IN CORD MEASURE 133 

applied to peeled wood by subtracting diameter of bark. The old 

Partridge rule used at Winchendon, Mass., computes the stacked volume 

of the log as (-D-)— with £) = diameter in feet. Each "cubic foot" 

by this rule is yts cord. The rule is thus based on stacked contents, 
and fractional cords are reduced to decimals by the divisor 128; e.g., 
64 " feet " would give .5 cord. 

To simplify this process the cordwood caliper rule known as the 
Humphrey Caliper ^ Rule, was divided into x^o of a cord; i.e., instead 
of measuring a stacked cubic foot the unit or j^q cord equaled 1.28 
stacked cubic feet. The scale stick for this rule was not marked off 
in inches, but for each standard length of stick the graduations repre- 
senting diameter were placed at the points which gave logs measuring 
a certain even volume (§ 80). Hence no fractional stacked feet were 
shown. 

Since oy either rule, the cubic contents of a cord is given as 100.5 

cubic feet, the Humphrey Rule by using the decimal system expressed 

f*iir)io Tppt 
the contents as — —— — within an error of but 0.5 per cent. The values 

of the rule thus correspond with those given for cubic contents of cylin- 
ders, but pointed off for two decimals. 

If we accept the standard of 100 solid cubic feet of wood as the 
maximum contents of a cord, the Humphrey Caliper Rule measures 
wood of any character or degree of straightness, surface, roughness, 
length or diameter not only by a uniform standard of cubic contents 
(as does the Partridge Rule) but directly in cubic feet, or in standard 
cubic contents. 

This rule therefore offers a double advantage. It is not only a cubic- 
foot standard, which is desirable for all scientific measurements of volume 
and growth, but it serves to standardize cord measure as well, on the 
basis of solid rather than stacked contents. The limitations in the 
use of the rule are the same as those of all caliper rules (§ 84). It can- 
not be applied to wood in the stack but only to pieces measured singly. 
Scale sticks made up for these values would enable measurements of 
cubic contents to be made directly for logs or trees to be used for vol- 
ume tables or other scientific purposes and would do away with cal- 
culation of cubic contents. This rule is used as the principal com- 
mercial standard in the vicinity of Keene, New Hampshire. It can be 
made up by anyone on the basis of diameter by applying the cubic 
contents of cylinders given in Table LXXVII, Appendix C. 

112. Discounting for Defect in Cord Measure. Pulpwood must be sound and 
free from rot or defective knots. Where logs of 8, 12 or 16 feet are measured by 
1 Invented by John Humphrey, Keene, N. H. 



134 



STACKED OR CORD MEASURE 



the cord, defective portions may be culled by subtracting from the total stacked 
volume, a piece whose volume is the square of the diameter in feet multiplied by 
length in feet. This deduction coincides with the basis of a standard cord of 
100.5 solid cubic feet and is based on Y2^g- cord for each cubic foot subtracted. 
This method is the basis of the following table: 

TABLE XXV* 

Measurements of 4-foot Round Spruce Pulpwood — with Cull Factors 
Based on Solid Cubic Contents 



Average 

diameter of 

stick. 


Solid contents of 
cord. 


Sticks per cord. 


Volume to be deducted 
for each stick culled. 


Inches 


Cubic feet 


Number 


Cubic feet 


3 


75.0 


375 


0.34 


4 


79.8 


228 


.56 


5 


83.6 


152 


.84 


6 


86.1 


109 


1.16 


7 


87.7 


82 


1.56 


8 


89.6 


64 


2.00 


9 


90.3 


51 


2.51 


10 


91.6 


42 


3.08 


11 


92.4 


35 


3.66 


12 


93.3 


29.7 


4.27 


13 


94.1 


25,5 


5.02 


14 


95.0 


22.1 


5.87 


15 


95.8 


19.6 


6.67 


16 


96.5 


17.1 


7.71 


17 


97.0 


15.4 


8.59 


18 


97.4 


13.7 


9.70 


19 


97.9 


12.4 


10.76 


20 


98.3 


11.3 


12.06 



* Prepared by H. L. Churchill for spruce in the Adirondack region, New York. 



Where the contents of the cord are expressed directly in soUd cubic 
feet, special tables can be worked up for deducting the actual cubic 
contents for sticks of given diameters. 

The Humphrey Caliper Rule will serve to make deductions based 
on solid measure, by scaling the contents of the defective portion as 
a stick of a given length and diameter. 

113. The Measurement of Bark. Bark, when used for tannin, is stripped off 
in sheets and piled in cords. At the factory a cord is measured by weight. Eastern 
hemlock bark must weigh 2240 pounds per cord, when dry. 

The bark peelers are paid by the stacked cord measure, which is in some 
localities 4 by 4 by 8 feet but more often is required to be full in one or more 
dimensions, according to local specifications. In New York, the dimensions are 



CONVERTING STACKED CORDS TO BOARD FEET 



135 



4 by 4 by 8 feet. In Upper Michigan, 4:1 by 4^ by S| feet is sometimes required, 
in order that the cord shall check out in weight. Others stijiulate 4^ by 45 by 8 
feet. In the West, hemlock bark is usually bought and sold by the standard cord, 
although weight per cord (2240 pounds) is sometimes used. Tan- bark oak is sold 
by weight.' 

Bark forms the largest per cent of total volume in young, small and rapidly 
growing trees, exposed to light and growing on dry exposed sites. It gives the 
smallest per cent of total volume on old, large trees, grown in dense stands, and 
on slow growing or suppressed trees. 

Mea.surement of bark in per cent of total volume of tree with bark, for the 
following species, show: 



• 

Species 


Character 


Per cent bark 


Southern yellow pine species 

Western yellow pine 

Yellow poplar, or tulip 


2-inch trees 

Diminishing with increased 

diameter 

12-inch trees 

Diminishing with increased 

diameter 
Diminishing with increased 

diameter 
Diminishing with increased 

diameter 

Diminishing with increased 

diameter 

All diameters 

All diameters 

All diameters 
All diameters 
All diameters 


40 

30 to 15 
24 

24 to 12 
15 to 12 


Ash 


22 . 4 to 10 . 3 


Hickory 


22 to 12 


Sugar maple 


Average 17 


Cottonwood 

Spruce, balsam, white pine, white 
birch 


Average 22 
Average 11 to 12§ 


Hemlock 


15 to 19 


Lodgepole pine 


Average 6 







The manufacturers of pulp, excelsior and products requiring peeled wood, 
when forced to purchase their raw material with bark on, soon determine the 
reduction factor required for their species and locality. The large and variable 
per cent of bark on loblolly pine in the South forces the purchaser of pulpwood 
stock to insist on peeling. 

114. Factors for Converting Stacked Cords to Board Feet. Where the output 
of wood in a given region, or for a given tract or ownership is in the form of both 
cordwood and sawlogs, it is often desirable to reduce cordwood to terms of its 
equivalent in board feet, in order to exjiress the total production in terms of a 
single standard. Less often, this conversion is desired as the basis of sale or 
contracts for logging. It is not the purpose of such conversion to determine the 
actual quantity of lumber which can be sawed from sticks of cordwood sizes and 
shapes. 



1 The standard cord in Oregon is 2300 pounds, 
is 2400 pounds . 



The standard cord in California 



136 STACKED OR CORD MEASURE 

The board-foot contents of a stacked cord depends first on the sohd cubic con- 
tents of the cord gather than its stacked measure, and second, on the diameter 
of the sticks which it contains (§ 54). Since soUd contents also depends on diam- 
eter of stick, the ratio of board feet to stacked contents increases with diameter 
from both sources, or much faster for stacked than for cubic volume. 

The diameter of the average stick is the determining factor in this ratio. The 
ratio itself will thus vary over a wide range depending on the class of wood handled. 
Crook and other irregularities of form have the same double effect as diameter, 
in reducing first the solid contents, and next, the board-foot contents per cubic 
foot of wood. The latter ratio can be determined for straight sticks by Table III 
(§ 41), Tiemann log rule, based on middle diameters, outside bark. For crooked 
sticks, a further reduction in ratio is required. 

To obtain the true ratio for a given cord of straight wood, it is necessary to 
determine first, the converting factor for solid cubic contents, and second, the 
average diameter of the sticks, at middle point outside bark. By use of Table III 
the converting factor from cubic to board feet is found for logs or bolts of this 
average size, and this multiphed by solid cubic contents gives contents of the 
stacked cord in board feet. 

But commercial log rules are based on diameter at small end and do not usually 
give actual sawed contents. For such ndes the ratio can be approximated directly 
by determining the average diameter and number of sticks in a cord, and scaling 
their contents with a log rule. 

The ratio for actual board-foot contents of cordwood diminishes to zero for 
sticks averaging from 3 to 4 inches in diameter, which is a common size for cord- 
wood. If so determined, the converting factor is not an indication of the real 
volume or utility of the contents of a cord of wood. For a given species and class 
of cordwood an arbitrary converting factor can bo obtained, based first on the 
per cent of solid cubic contents of a cord of sticks of average diameter and second, 
on an average or fair ratio between board feet and cubic feet, and not on the ratio 
for the actual small or irregular sizes. For instance, western juniper cordwood 
gives about 60 cubic feet per cord. Adopting a fairly low ratio of 46 per cent or 
5.55 board feet per cubic foot of total solid contents, the board-foot converting factor 
is 60 times 5.55 or 333 board feet per cord, or 3 cords per 1000 board feet. For 
white pine, 100 cubic feet per cord, with nearly the same ratio, 5.5 board feet per 
cubic foot, gives 550 board feet per cord. The ratio of 500 board feet per cord 
adopted by the U. S. Forest Service for pulpwood gives 5.55 board feet per cubic 
foot for wood yielding 90 cubic feet per cord, which is a fair average for well-shaped 
sticks. 

It would appear then that the factor 5.55 has some merits as a universal con- 
verting factor and that the variation of board-foot converting factors for entire 
cords should be based on the difference in cubic contents of the cord rather than by 
the adoption of variable ratios between board feet and cubic feet. This practice 
is sound. The factor 5.55 corresponds to the actual sawed contents of a log 
between 7 and 8 inches in diameter at middle of stick inside bark. The basis 
of this ratio is comparison between total cubic contents including taper, and actual 
sawed contents. Commercial log rules deal with reduced values for both cubic and 
sawed output, using the contents of the small cylinder for the one, and neglecting 
over-run in the other. These two reductions may not be of equal weight, but tend 
to give approximately equal ratios to those stated. 

If the average diameter of logs exceed 71 inches at middle, inside bark, the actual 
ratio is correspondingly larger. Only in this way can ratios as high as 575 board 



WEIGHT AS A MEASURE OF CORDWOOD 137 

feet per cord, used on the Pacific Coast, be obtained. The ratio in New England 
for pulp wood is 560 board feet.' 

115. Weight as a Measure of Cordwood. For fuel, weight is a 
better measure of the value of cordwood than solid cubic volume, and 
of still greater utility for the measurement of stacked volume. Its 
merits increase with the increasing irregularity of form in sticks which 
render the determination of solid contents of stacks so uncertain. But 
one factor operates against the substitution of weight for stacked 
measure, for fuel wood, and that is the unfamiliarity of the public with 
the proper standard weights which should constitute a cord. This 
is due first to the great variation in weight between wood of different 
species, a variation which would be equalized as to -price if equal weights 
regardless of bulk commanded approximately the same price, and second, 
to the great difference in weight between green and air-dried wood. 
If sold by weight, dealers would endeavor to sell the wood as green as 
possible. Green wood has less net fuel value per pound, not only 
because the purchaser pays for water instead of net dry weight, but also 
because each pound of dry wood has to generate heat enough to vaporize 
all the water in the wood and only the surplus heat is given off. 

But for dead dry juniper or pinon or mesquite roots or for well- 
seasoned woods difficult to measure in bulk, weight is practically the 
universal standard. Dealers customarily deliver from 200 to 400 
pounds less of weight per cord than the actual weight of an average 
cord of such wood. For instance, pinon should weigh 3000 pounds 
per cord, but it is often sold at 2000 pounds per cord. It would be 
better to substitute weight altogether and not maintain the pretense 
of delivering a cord by measure. This would place the dry wood 
on the same basis as coal. 

Air-dried wood still contains from 15 to 20 per cent moisture. The 
variation in per cent of water in green wood compared with dry wood 
is extreme, as illustrated by Table LXXXIII (Appendix C). 

References 

Factors Influencing the Volume of Solid Wood in the Cord, Raphael Zon, Forestry 

Quarterly, Vol. I, 1903, p. 126. 
Untersuchungen liber die Festgehalt und das Gewicht des Schichtholzes und der 

Rinde, F. Baur, Augsburg, 1879. 
Mitteilungen aus dem Forstlichen Versuchswesen Oesterreiches, 1877-1881, Report 

by Von Seckendorff. 
Paper Birch in the Northeast, S. T. Dana, U. S. Forest Service Circular 163, 1909, 

pp. 34-3.5. 

' In Forest Mensuration of White Pine in Massachusetts, p. 4.5, ratios for white 
pine 1-inch lumber are given, running from 488 board feet for 5-inch logs to 730 
board feet for 24-inch logs, measured at middle of log outside hark. 



138 STACKED OR CORD MEASURE 

Second Growth Hardwoods in Connecticut,' E. H. Frothingham, U. S. Forest 

Service Bui. 96, 1912, pp. 63-64. 
The Northern Hardwood Forest, E. H. Frothingham, Bui. 285, U. S. Dept. Agr., 

1915, p. 62. 
Balsam Fir, Bui. 55, U. S. Dept. Agr., 1914, p. 52. 
Measuring Cordwood in Short Lengths, R. C. Hawley, Journal of Forestry, Vol. 

XVn, 1919, p. 312. 
A Practical Xylometer for Cross-ties, F. Dunlap, Forestry Quarterly, Vol. Ill, 1905, 

p. 335. 
A Practical Xylometer, J. S. Illick, Journal of Forestry, Vol. XV, 1917, p 859. 



PART II 
THE MEASUREMENT OF STANDING TIMBER 



CHAPTER X 
UNITS OF MEASUREMENT FOR STANDING TIMBER 

116. Board Feet — Basis of Application. The value of standing 
timber must be determined as a basis for sale either of the timber alone, 
or of the land and the timber. This value depends upon the quantity 
of wood which may be cut from the tract, but still more upon its value 
per unit of volume. As set forth in Part I, the contents of logs and 
trees in North America are expressed, whenever possible, in terms of 
the final products instead of by cubic volume as in Europe. Standing 
timber, therefore, is commonly measured in terms of board feet, cords, 
or pieces such as poles, piles or railroad ties and is rarely expressed as 
cubic feet, since it is seldom sold on that basis. If estimated by cubic 
feet, the contents are usually' converted into their equivalent in cords. 

When the board-foot unit is used in timber estimating, the basis 
of determining the contents of the standing timber must be identical 
with that on which the timber is to be sold when cut. 

If manufactured on the tract by small portable mills, the actual 
sawed output in lumber, the mill cut, furnishes this basis. When 
round-edged lumber is sawed and small trees utilized to a small top 
diameter (§21) the yield in board measure may be 100 per cent greater 
than when the " sawlog "-sized timber only is merchantable, as in 
large logging operations. 

When scaled and sold in the log, the estimated contents of the stand, 
before cutting, should coincide, not with the sawed output, but with 
the log scale. Since different log rules give different scaled contents 
for the same logs, the estimate must be based upon the log rule which 
wUl be used to scale the logs. Hence an estimate made on the basis 
of the Doyle rule will differ from one based on the Scribner rule or the 
International rule. In all large logging operations where the logs 
are transported some distance to the mill, timber is estimated solely 
on the basis of the standard log rule in use. 

139 



140 UNITS OF MEASUREMENT FOR STANDING TIMBER 

Local log rules based on mill tallies may be substituted for the sawed 
product as the basis of estimating timber on small tracts. 

No such difficulties affect the estimating of timber in terms of cubic 
units or cords, which include the entire contents of all trees within the 
merchantable limits of size, up to the merchantable limit in the tops. 

117. The Piece. Poles or piling usually comprise the entire mer- 
chantable portion of the trees which produce them, but can only be 
cut from trees having the specified dimensions. Familiarity with these 
specifications enables the cruiser to count the number of pieces in the 
stand, and to tally them in separate classes. The same method may 
be used in estimating standard railroad ties, but in this case the number 
of ties in each tree must be counted separately in accordance with the 
five standard grades (Appendix B, § 369). Where the tree is large 
enough to produce more than one standard tie from a single 8- or 8|- 
foot length, the cruiser must rely either on his knowledge of the contents 
of the bolt in ties, or refer to a volume table for piece products (§ 162). 
He gets the total tie count for the tree by adding the contents of each 
separate bolt, up to a point where the diameter is too small to produce 
another standard tie. Posts are counted in the same way but, owing 
to their smaller value and greater numl)ei', the count is usually more 
or less of an approximation. The same system may be used, if required, 
in estimating the quantity of mine timbers and mine ties in a stand. 
Products such as stave bolts, which demand a high quality of timber 
practically free from knots and all forms of defect, and are of small 
size, introduce two features common to estimating in board feet, namely, 
a table of volumes, and discounts for cull. Stave timber for staves 
of given sizes may be estimated by knowing how many staves may 
be cut from bolts of given dimensions. The number and size of the 
cuts in each tree will give their sound contents, from which are deducted 
all visible defects. A liberal allowance is also made for invisible defects 
in the interior of the tree. 

Since only a portion of a stand is converted into these forms of 
product, the estimating of piece products may be only a part of a 
general estimate in which the remainder of the stand is measured 
either for logs or for cordwood. 

118. Choice of Units in Estimating Timber. Methods of timber 
estimating are determined by the cruiser's choice as to whether he will 
deal directly with one of four units, namely, the stand as a whole, the 
individual tree, the individual log, or the piece (§ 117). Any one of 
the first three methods may be used when the volume of the stand 
is expressed in terms of cubic units, or in board feet. If the tree or 
log is not used, the stand is considered as a whole and a direct guess 
or estimate is made of its total contents (§ 206). If the tree or the log 



THE LOG AS THE UNIT IN ESTIMATING 141 

is used, the method requires a count and tally by different sizes, and 
gives rise to many systems of estimating, depending on whether the 
entire area or only a portion of it is to be counted. 

119. The Log as the Unit in Estimating, When the product to 
be estimated in board feet is lumber, the log becomes a convenient 
and much used unit for estimating. Lumber is measured or scaled 
in the log by a given log rule. The contents is given for logs according 
to their diameter inside bark at small end, and length. Hence a tally 
of the top diameter inside bark and the length of each log in a tree, 
and the use of a log rule, will give the board-foot contents of the tree. 
If every log is so tallied the stand is measured by merely totaling the 
contents of the logs, without computing the volume of separate trees. 

No further volume basis is needed in this method than the log 
rule or scale stick. But the cruiser must know the amount of taper 
in each log, the thickness of bark to be deducted, and the log length 
to use in estimating. 

Log lengths as actually cut are determined by the crooks and other 
peculiarities of each tree. But in estimating timber, these variable 
log lengths are disregarded and a uniform or standard length is adopted 
which conforms within reasonable limits to the average log length most 
frequently used. For eastern conifers this is 16 feet, while hardwoods 
may require 12 feet. On the Pacific Coast, 32 feet is used by man}^ 
cruisers. If logs when cut average shorter than the standard, the 
scaled contents of the logs will over-run the estimate, while if longer 
logs are cut, the scale will fall short (§ 83). 

The method of tallying the logs in a tree is as follows : 

1. Estimate or measure the diameter of the butt log either at the 
stump, at 4| feet from the ground, or at 1 foot above the butt swell, 
choosing one of these methods to the exclusion of the others. Foresters 
use 4| feet as the accepted standard. 

2. Deduct the double thickness of bark to obtain the diameter, 
inside bark, at this point. 

3. Estimate the number of inches to deduct from this diameter for 
taper, to obtain the diameter at the top of the first log of standard 
length. This and all upper estimates of diameter are inside the bark. 

4. Estimate by eye the number of standard logs in the tree, to the 
limit of merchantable size. The top diameter at this point should 
be known or estimated, inside bark. 

5. From the diameter of the top of the first log, inside bark, deduct 
successively the estimated taper, in inches, to obtain the diameter 
of each remaining log. 

An alternate plan frequently used is to measure the diameter out- 
side bark at the butt, or at 4| feet, subtract the taper outside bark 



142 UNITS OF MEASUREMENT FOR STANDING TIMBER 

for the first log, and then subtract the estimated thickness of bark at 
this point, or at the top of the first log instead of at the butt. 

A third plan is to estimate directly the diameter, minus bark, at 
the top of the first log, without measuring the butt. Or, a table may 
be prepared showing diameter, inside bark, at the top of the first log, 
for trees of different diameters at 4| feet. 

Each of these plans aims to secure the diameter, inside bark, at 
the top of the butt log as the basis from which to figure the top diam- 
eters of the remaining logs. 

The eye may be trained to estimate log lengths and taper by the use of a pole 
with a cross-piece at the top, marked off in inches. The length of pole (about 
12 feet) permits holding the cross-piece at the height of the top of the first log 
plus an allowance for height of stump. By comparison with this measured length, 
the number of logs in the upper bole may be estimated by eye. By measuring 
the tree at 45 feet, and reading the cross-arm, the taper, in inches, for the butt 
log is shown. Bark thickness is then subtracted as determined for the species 
by observation on felled trees or logs. This varies for the top of the butt log, 
from 2 inches to 1 inch for most species. The total number of logs, to the limit 
of merchantable diameter, gives the total taper to that point. If 6 inches is the 
merchantable limit, this diameter, subtracted from that of the top of the butt 
log inside bark, indicates the taper to be distributed between the upper logs. 
Bearing in mind the tendency to more rapid taper in the crown, the actual taper 
of each log can be approximated with reasonable accuracy and its diameter inside 
bark recorded. Two men usually work together in this practice, or in training. 
One man may use the method if the pole is made long enough to be leaned against 
the tree (17 to 18 feet), while he gets far enough off to judge its height. 

This method assumes that the eye can be trained to judge diameters 
to an inch, at varying distances and heights above ground. But in 
timber estimating only the general character of the tree is noted, and 
its total height, or the number of standard-length logs. The taper 
of the successive logs is obtained from measuring the diameters of 
felled or wind-thrown trees of the same character as the standing timber. 
The taper for a 16-foot log may vary from 1 to 10 inches or even more, 
depending on site, density of stand, butt diameter, and position of the 
log in the tree. 

Many cruisers assume that once the difference in diameter between 
the top of the second and the first log is ascertained or assumed, each 
successive upper log will have an equal taper, giving to the tree a uniform 
taper per log of 2, 3 or more inches. They know that the butt log 
will taper more rapidly than the second log, but the above practice 
ignores the taper of the butt log. 

They also know that as soon as the green crown is encountered, 
the taper per log again increases. But in regions where rough logs 
in the crown are seldom utilized, this assumption of a uniform taper 
for the second and higher logs in the bole is approximately correct. 



LOG RUN OR AVERAGE LOG METHOD 143 

Where greater accuracy is sought, and especially, where the diameter 
of the tree is measured at 4^ feet rather than guessed at, tables may 
be compiled from the actual measurement of the upper diameters of 
felled trees which show the average taper for each log, for trees of given 
diameter and height, and with the width of bark actually measured 
and deducted for the top of the butt log. These tables will enable 
the cruiser to tally the sizes of his logs without relying on his eye for 
more than the determination of total height or number of logs. 

Log grades (§87), when used in timber estimating, require the tally 
of the top diameter of the logs, separated into grades. This permits 
of the separate totaling of volume in each log grade on the tract. 

120. Log Run or Average Log Method. The tallying of the actual 
size of every log on a tract is so slow and expensive that it is possible 
only when the timber is large and scattered. Woodsmen, who use the 
log as the unit of estimating, do not usually tally any sizes but obtain 
the total number of logs on the area by five steps, namely: 

1. A count of the trees. 

2. Decision as to the average number of logs per tree. This may 
be in halves or even quarters, as 3j logs per tree, referring of course 
to the standard length adopted for estimating. 

3. The board-foot contents of an average log. 

The last point is based on familiarity with the results of scaling logs 
cut from similar timber, and the cruiser expresses it in terms of " log 
run " or number of logs required to scale 1000 board-feet of lumber, 
as illustrated by the following figures: 

Log Run. Contents of Average Log. 

2 per 1000 board feet. 500 board feet. 

5 per 1000 board feet. 200 board feet. 

10 per 1000 board feet. 100 board feet. 

20 per 1000 board feet. 50 board feet. 

40 per 1000 board feet. 25 board feet. 

The " log run " increases as the average log content diminishes. 
Knowing the log run, or guessing at it, the estimate in board feet is 
obtained by: 

4. Multiplying the total number of trees by the number of logs per 
tree. 

5. Dividing the total number of logs by the log run or number of 
logs in 1000 board feet of lumber. 

This method was used l)y many old-time cruisers in the Lake States 
region to the exclusion of all others. When old and young, or large 
and small timber is found on the same tract, separate classes are usually 
made in the count. 



144 UNITS OF MEASUREMENT FOR STANDING TIMBER 

121. The Tree as a Unit in Estimating. Volume Tables. The 

necessity for combined speed and accuracy to reduce the cost and 
increase the reliability of timber estimates has led to the almost uni- 
versal substitution of the tree unit for the log unit. Instead of entering 
the size of each log separately, the dimensions of the entire tree are 
noted. 

This requires that the volume of entire trees of the sizes tallied be 
previously known. The sum of the volume of the logs which they con- 
tain gives this information. A table, in which the average volume 
of trees of given sizes is shown, is termed a volume table, in contrast 
to a log rule or log table, which gives only the contents of single logs 
and never that of entire trees. 

To avoid confusion in these terms, it should be noted that the stand- 
ard definitions are: 

For a log- volume table — the term, Log Rule. 

For a tree-volume table— the term, Volume Table. 

The latter term should never be used by foresters to mean the 
contents of logs, although the term log table may be used. The term 
" volume table " always refers to the volume of trees, being substituted 
for the longer descriptive term, Tree-volume Table. 

Timber cruisers were slow to see the advantage of thus tabulating 
or summing up the total volumes of trees in systematic form. They 
either adhered to the log basis, or in the instances when they used the 
tree volume as a unit, merely calculated this for " average " trees by 
mentally summing up the contents of the logs in individual trees, and 
from the general knowledge thus obtained, assuming that trees in a 
given stand averaged or " ran " a certain volume per tree. This method 
was universally used in the South, where the Doyle rule readily lent 
itseK to quick mental computations of the contents of 16-foot logs 
(subtract 4 inches from the diameter inside bark, and square the 
remainder for board-foot contents of log, § 65). The total count of 
trees, multiplied by the average contents per tree, gave the estimate. 

122. Volume Tables Based on Standard Tapers per Log. " Uni- 
versal " Volimie Tables. In the Pacific Northwest, the great height 
of the trees and consequent large number of logs in each tree, and 
the relatively few trees per acre, each with a large volume, soon brought 
a realization of the need for substituting the tree unit for the log. The 
difficulty of mentally computing the contents of trees varying so widely 
in volume forced the use of the volume table, in which was recorded 
the total volumes of trees of all sizes. These cruisers' volume tables, 
of which several have been constructed, are, in most instances, based 
on the principle of uniform taper per log, varying from 2 to 10 inches. 
The contents of successive logs, as scaled by the accepted log rule, 



VOLUME TABLES BASED ON STANDARD TAPERS PER LOG 145 

diminishing in top diameter by the indicated taper, are totaled, and 
the sum taken as the vohuiie of the tree. These computations do not 
require the measurement of the tree but are performed in the office 
from the log rule. 

The volumes in such a table are the scaled contents of logs by a given log rule, 
and will apply only to regions where this same log rule is used. But it is a simple 
matter to compute a new table for any other log rule, by the same method, since 
no field work is required. Wherever the log rule is the standard, such a table is 
applied to all species, types and character of trees, and in this sense is universal. 
The assumption underlying such a table is that the merchantable portion of all 
trees have the shape of the frustums of cones, hence the determination of the three 
factors, average taper per log, diameter at top of first log, and number of logs in 
the tree, determine the scaled contents of the tree as given in the table. As shown 
below, the assumption is not correct. 

In applying this table, these cruisers seldom attempt to tally the dimensions 
of each tree. The trees are counted, separately by species, and also by classes, 
as large, medium or small. Then the average diameter, average number of logs per 
tree, and average taper per log is decided on usually by guess or by judgment. 
The volume table merely serves to give the assumed volume of a tree of this 
diameter, height and taper. The estimate or total for the species is obtained by 
multiplying this volume by the tree count. 

The advantages of obtaining a universal and elastic volume table, applicable to 
any species, region and character of timbers are self-evident. The defects in 
uniform or universal volume tables based on the frustums of cones are: 

1. The form of the average tree of any species, when the merchantable portion 
only is considered, resembles more nearly the frustum of a paraboloid than that of 
a cone (§ 26). While the merchantable portion may be treated as the frustum of 
a cone, yet investigation shows that the average volume of trees of different species 
and diameters is usually either less or greater than that assumed by the table. 
This possible error is consistently neglected. 

2. For accurate application, the universal table requires the determination of 
three dimensions for every tree whose volume is to be ascertained, namely, diam- 
eter, height and taper. A tally of every tree by diameter and height is possible, 
but the separation of a third factor, tree by tree, makes the tally too complicated, 
and requires the substitution of average tapers for a species, or for groups of 
diameters as indicated above. But the trees in any given stand or area never taper 
uniformly. The larger trees have the greater taper. Those growing in dense 
stands have the least. No average can be found which will apply even to the 
trees of one diameter class, much less to trees of all classes. The assumption of a 
definite taper for the trees on a plot will tend to over-estimate the volume of trees 
larger than the selected average tree, and under-estimate those of small diameter. 
Whether these errors balance depends more on luck than on skill. 

3. The use of such a table presupposes the system of counting rather than of 
tallying each tree, and assumes the risk of error in selecting, largely by eye, an 
average tree which, when multiplied by the count, will give the approximate 
estimate. It does not lend itself to an accurate inventory of the timber, tree 
by tree, in which the diameter and merchantable length of each tree is 
recorded. 

4. Since such tables assume that upper diameters differ by gradations of 1 inch 
per log, a 4-log tree will show top diameters in the table differing by 4-inch classes, 



146 



UNITS OF MEASUREMENT FOR STANDING TIMBER 



while the average taper may be somewhere between these limits and the volume 
be given incorrectly by either the upper or lower class. A tree 20 inches at the top 
of the first log will be classed as having a taper per log of 1 inch, 2 inches or 3 inches. 
At the top of the fourth log, the first tree will measure 17 inches, the second tree, 
14 inches, and the third, 11 inches. The actual average top diameter may fall at 
12 inches or at 15 inches. 

123. Substitution of Mill Factor for Log Rules in Universal Tables. In the 
above tables, the contents of the logs are determined by the standard log rule 
used in scaling. Dr. C. A. Schenck substituted what is termed the mill factor 
for the log rule, thus basing the volume of the tree upon the sawed output (§ 116). 
Assuming, as a basis, that the cubic contents of the cylinder measured at the small 
end of the log, when multiplied by 12, gives the maximum board-foot contents 
(§ 12), the waste for slabbing, edging and saw kerf, independent of taper, which is 
not considered, will reduce this output to from 8 to 5 board feet per cubic foot. 
The per cents of cubic contents of the cylinder based on small end of log, which 
these mill factors represent are: 







Scaled contents of 




Cubic 


nearest equivalent 


Mill factor 


contents. 


log rule 
(Table II, §38). 




Per cent 


Per cent 


8 


661 


Vermont (63.4) 


7 


581 


Calcasieu (57.8) 


6 


50 


Orange River (50.9) 


5 


41f 


Delaware (42 . 4) 



An example of these mill-factor tables is given on page 147, for logs 16 feet long: 

To determine these values the volume in cubic feet of the cylinder was mul- 
tiplied by 5, 6, 7 and 8 respectively. These tables give the cruiser the oppor- 
tunity to substitute a fixed per cent of utilization, as indicated above, for a log 
rule. The other three variables remain the same, namely, diameter, number of 
logs and rate of taper per log. 

It is assumed that the mill factor can be chosen to suit the local conditions of 
milling, the factor 8 or 665 per cent representing the use of band saws in large mills, 
while the factor 5 approximates the conditions in small local circular-saw hard- 
wood mills, thus making the cruiser independent of log rules. This apparent 
advantage is nullified by two serious defects: First, the taper of the log is neglected, 
and this frequently produces a mill factor of 10 for large logs. Second, the board- 
foot contents is assumed to vary directly as the cubic contents, so that the tables 
force the use of log rules based on cubic rather than sawed products and introduce 
the errors of this method. Mill factors increase directly with the average diameter 
of the log independent of mill practice. It is not sufficient merely to know the 
general character of the milling, but the sizes of the timber must also be known. 
An average mill factor based on both of these variables may be seriously in error 
and the use of different mill factors for logs or trees of different sizes is apparently 
necessary to secure accuracy. The use of these tables is therefore not as satis- 
factory as their apparent simplicity seems to indicate. 



VOLUME TABLES BASED ON ACTUAL VOLUMES OF TREES 147 



TABLE XXVI 

A Portion of a Volume Table Based on Mill Factors 
Trees measuring 9 inches at top of first 16-foot log, inside bark 





Mill factor 


Taper per Log 


16-foot 
logs 


1 inch 


2 inches 3 inches 


4 inches 




Board feet 




5 


31 


31 


31 


31 


1 


6 


37 


37 


37 


37 


7 


43 


43 


43 


43 




8 


57 


57 


57 


57 




5 


55 


49 


45 


40 


2 


6 


66 


59 


54 


48 


7 


77 


69 


62 


57 




8 


89 


79 


71 


65 




5 


74 


59 






3 


6 


«9 


71 






7 


104 


83 








8 


118 


95 







124. Volume Tables Based on Actual Volumes of Trees. Volume 
tables as used by foresters are based on the measurement of the actual 
contents of entire trees, and not upon assumed regular taper or conical 
form. The tree contents or volume table may give, 

Entire cubic contents of stem, with bark, or without bark. 
Merchantable cubic contents of stem, or of stem and larger 

branches, with or without bark. 
Merchantable contents of stem in terms of 
Board feet 

By a given log rule. 

By mill tally, under given conditions of sawing. 
Other units, such as 
Standard cross ties. 
Poles, or posts. 
Staves or headings. 
Cords, usually converted from cubic feet. 



148 UNITS OF MEASUREMENT FOR STANDING TIMBER 

Combination Volume Tables giving the merchantable volume in 
Ties, and residual cords. 

Board feet, and residual cords and other combinations. 
Graded Volume Tables, giving the volume in 
Board feet, by lumber grades. 
Logs, by log grades. 

The use of the last-named type has not yet been attempted. 

Volume tables of this character make possible the tallying of every 
tree, eliminate the risk of averaging the dimensions or volume of trees 
counted, and require of the cruiser only the recording of diameters 
and of heights, and discounts for defect. 

Since trees vary so widely in form, height and taper, and the table 
is implicitly relied on to give correctly the variable volumes caused 
by these factors, without measuring the taper, the use of such tables 
and their reliability or accuracy must be thoroughly understood, or 
it may easily lead to errors of greater magnitude than those incurred 
by an experienced cruiser using the universal ** taper " table for volumes 
(§149). 

The greatest drawback in the use of specific volume tables is the 
number of tables required, and the cost of their preparation. Species 
may differ from each other in form or bark thickness, so as to require 
separate volume tables. Substitution of a table made for one species 
for use with a different species is justifiable only when research has 
shown the two species to possess the same bark thickness and average 
form. 

Tables made for one unit of measure, or even for a given log rule 
are not serviceable for a different unit or log rule. Tables of merchant- 
able volume, accurate for a given standard of tree utilization, become 
obsolete when a closer standard is adopted. For these reasons, and 
owing to the great number of species, range of conditions, difference in 
log rules, and variety of products, the cruiser entering a new region 
is usually confronted with a lack of tables, and is driven to adopt 
either the universal taper system, or the log, as his means of estimating 
volumes. The adoption of a universal cubic-foot basis for volume 
would greatly simplify the problem of volume tables. 

125. The Point of Measurement of Diameters in Volume Tables. 
Either of the above types of volume table shows volumes for trees of 
given diameters and heights. The diameter must be measured near 
the base of the tree, where it can be reached with calipers or tape. 
But there is no regularity about the flare of the butts of trees, for this 
is determined by exposure to wind strain, by the size of the bole, the 
site and the species. Butt swelling increases more rapidly with age 
than does the diameter of the bole, so that the older and larger the tree, 



DIAMETERS IN VOLUME TABLES 



149 



the more pronounced this swelhng, and the further it extends up the 
trunk. Tree volumes nmst be averaged on the basis of their diameter 
in inches. If this diameter is taken at some point on the butt swelhng, 
a tree with a rapid butt swelling will have a far smaller volume than 
one of the same stump diameter and a gradual swelling, as is illus- 
trated in Fig. 24 by trees A and B. But if these diameters were taken 
at a point above the butt swelling the two trees would properly fall 
into different classes. Since it is necessary to put in a single class 
trees whose volumes are as nearly similar as possible (trees A and C), 
the practice of classifying these trees by their diameter on the stump 
is inaccurate. The height of stump itself is also a variable. Tables 



(Vwl 



4M 



12 





yv\ 



18" 



12' 



IG" 



Fig. 24. — Comparison of stump height and breast height as points of measurement 
to determine the diameter of standing trees. 



based upon '' diameter at the stump," which do not indicate at what 
height this diameter is measured, are difficult to apply and unreliable. 
For very large trees with excessive butt swelling such as cypress, 
or many West Coast species, the diameter classes should be based 
upon measurements taken above this swelling. A standard form of 
universal table used on the Pacific Coast is based on a butt measure- 
ment to be taken 1 foot above the point where the butt swelling ceases. 
The disadvantage of measuring at a variable height is considered as 
offset by the merit of avoiding this variable factor of butt swelling. 
In cypress, one typical table was based on diameter at 20 feet from 
the ground and cruisers customarily estimate cypress trees from the 
diameter obtained above the butt swelling. 



150 UNITS OF MEASUREMENT FOR STANDING TIMBER 

For most species, the point 4| feet above ground has been accepted 
by foresters for measurement of diameter as it falls above the swell- 
ing and at a convenient height for use of calipers. This height is also 
used in England and India. In Continental Europe, 1.3 meters, or 
4.3 feet, is the standard height. 

This measurement at 4| feet is termed diameter breast high, and 
is abbreviated both in speech and record to D.B.H. Measurement 
outside bark is always indicated by the abbreviation. 

In the Philippines and other tropical countries it will be impossible 
to use a similar height for many species owing to the development 
of buttresses on the trunks. Such species will probably have to be 
measured either above the flare, or at a height of 16 to 20 feet, by 
eye, using the 4| foot standard point only for species and types which 
permit it. 

Where D.B.H. is adhered to for species like Western larch, red 
cedar or Douglas fir. on the Pacific Coast, butt swelling greatly inter- 
feres with the uniformity of the volumes for these species for trees of 
given diameters when compared with other species like western yellow 
pine whose swelling seldom reaches this height. This apparent dif- 
ference in volume may be from 20 to 40 per cent in favor of the pine. 

126. Bark as Affecting Diameter in Volume Tables. For species 
whose bark is of uniform thickness for trees of the same D.B.H., the 
diameter taken outside the bark is preferable as a standard of classi- 
fication to diameter inside the bark. The cruiser has no time to measure 
bark thickness except on occasional test trees. The width of bark, 
however, is seldom uniform. For trees of the same diameter, it is thick- 
est on exposed and on rapidly growing trees, and thinnest on sheltered, 
crowded and slow-growing or suppressed trees (§ 113). The larger 
the trees, the greater the actual thickness of bark, and the wider the 
possible variation in thickness. This thickness may range from 2 
to 5 inches and over, on West Coast species. Volume tables based 
on diameter inside bark, therefore, are more consistent and accurate 
as tables, than those based on outside bark measurement. 

But this would require the tallyman to throw off the double width 
of bark from every tree tallied. The experienced cruiser, who deals 
with single average trees only, can from his experience throw off the 
proper average width of bark for the selected tree, increasing the deduc- 
tion for open and exposed situations and vice versa. There is no 
such choice in the tally of every tree. The mistakes made in mental 
arithmetic and the errors in guessing the proper width of bark to allow 
would be more serious than discrepancies in the table. In practice, 
then, D.B.H. would have to be recorded and average bark thickness 
afterwards deducted previous to computing the volume. 



CLASSIFICATION OF TREES BY DIAMETER 151 

Species with thick bark will show a smaller volume for the same 
diameters than those with thin bark, because of taking the diameter 
on the bark surface and not on the wood. Individual trees with thick 
bark will give correspondingly less volume than the average for the 
diameter class shown in the table. Timber on exposed sites will be 
over-estimated by tables based on diameter outside bark unless con- 
structed locally for the same sites. Width of bark, therefore, is a cause 
of variation in the attempted standardization of volume by diameter 
classes, which is eliminated in the universal tables when these are based 
on diameter inside bark, at either top of log, D.B.H., or stump. 

127. Classification of Trees by Diameter. Standard volume tables 
are commonly based on D.B.H. outside bark. The actual diameter 
of trees can be measured as closely as the nearest i^-inch. The aver- 
age of two measurements taken at right angles is considered the diam- 
eter of the tree. 

For felled trees whose volume is to be measured in the construction 
of volume tables, the diameters are recorded to the nearest actual 
xV-inch. But these volumes are classified later by 1-inch, or 2-inch 
classes. One-inch classes have been adopted as standard for Eastern 
species, while in the West, owing to the greater range of diameters 
encountered, 2-inch classes are deemed sufficient. Each 1-inch class 
includes all trees whose average D.B.H. is above .5 in the inch below, 
and .5 and under in the given inch class; e.g., the 9-inch class includes 
trees measuring 8.6 to 9.5 inches. In 2-inch classes, the even inch is 
used. A 10-inch class would include trees measuring 9.1 to 11.0 
inches. 

128. Classification of Trees by Height. Height is never used as 
the sole basis of tree classes; diameter is the fundamental basis of 
classification. But height exerts an enormous influence on the volumes 
of trees of the same D.B.H., the extreme difference in volumes for dif- 
ferent heights being more than 100 per cent. These differences in height 
and volume for trees of the same diameters occur in stands of different 
density, growing on different qualities of site, or at different altitudes. 
They correspond with differences in the average taper per log, as dis- 
tinguished in universal volume tables. 

It follows that the separation of trees of a given diameter class into 
several height classes previous to averaging their volumes is another 
way of distinguishing between trees of gradual and of rapid taper, 
and that if enough of these height classes are made, the differences in 
volume due to more or less rapid taper are distinguished even more 
accurately than by introducing taper as a factor in the table. The 
height, rather than any arbitrary amount of taper, is the real basis of 
classification, and the actual average volume, rather than an assumed 



152 UNITS OF MEASUREMENT FOR STANDING TIMBER 

volume, is then expressed in the table. The rate of taper for trees in 
different height classes within any diameter class, as 20 inches D.B.H., 
need not be shown in such tables. If measured, it will be found to differ 
by arbitrary fractions of inches instead of by exact 1-inch classes per 
standard log. 

Height classes may be based on total height, or on the length of the 
merchantable bole. In the former case, height classes are based on 
either 5- or 10-foot gradations, using the same system of rounding 
off as for diameters, e.g., the 70-foot height class with 10-foot gradations 
includes all trees 66 to 75 feet in height. With 5-foot gradations, it 
includes trees 68 to 72 feet in height. When merchantable heights 
are used, these lengths are commonly standardized to conform to a 
common log length such as 16 feet and expressed as 1, 2, 3 or more log 
trees. The log length used is always stated. Half-log lengths may be 
differentiated. With valuable hardwoods of variable merchantable 
length, there is some need for closer classification of merchantable 
lengths, but volume tables are seldom constructed for intervals of less 
than 8 feet. 

129. Diameter Alone, Versus Diameter and Height, as Basis of 
Volume Tables. To separate or classify the volumes of trees of each 
given diameter class into from 4 to 10 height classes requires the measure- 
ment of from 250 to 1000 trees, in order that the average volume in 
each of these numerous classes may be found with some accuracy 
(§ 137). This makes it impossible to take the time to construct such 
tables for local or immediate use. Hence many volume tables have 
been based on diameter alone, averaging together trees of all heights. 
Sometimes the average heights of the trees of each diameter class are 
shown, often they are omitted. 

For timber of uniform age and density of stand and growing on the 
same quality of site, individual trees of the same diameter will still 
differ considerably in height and volume; yet an average height for 
each diameter may be found, which will indicate quite closely the 
average volume for that particular stand or type and age class. But 
such a volume table is quite worthless for application to any other 
stand, age class or type, unless it can first be shown that the average 
heights based on diameter are the same in both cases. Lacking, 
first, the knowledge of the average heights used in the table, and second, 
the demonstration that these coincide with those of the stand to be 
estimated, the only possible procedure is the preparation of an entirely 
new volume table. 

But with a table based on a classification of heights and correspond- 
ing volumes under each diameter class, stands of any degree of density 
or age, and growing on any site, may be estimated by use of this table, 



STANDARD VERSUS LOCAL VOLUME TABLES 153 

if the volumes taken from the table are those for heights correspond- 
ing to the trees in the stand. 

130. Standard Versus Local Volume Tables. Volume Tables based 
on both diameter and height classes, in whose construction from 500 
to several thousand trees have been used, selected from as wide a range 
of sites and locations as possible, are termed Standard Volume Tables, 
while those based on diameter, either alone or with the average height 
of trees of each diameter class stated, and applicable only to a given 
stand or site, are known as Local Volume Tables. 

It follows that local volume tables applicable to any stand, age 
or site can be derived from the values given in a standard volume table 
and can be expressed on the basis of diameter alone by first determin- 
ing, for the stand, the average height to use for each diameter class. 

Classification by both diameter and by height is not sufficient to 
secure complete accuracy in volume tables because of differences in 
average form (§ 166). But such tables, well constructed, are vastly 
more accurate than any universal table based on uniform tapers, or 
frustums of cones, and are known to apply with almost the same degree 
of accuracy throughout the entire range of a species. Greater vari- 
ation in form and volume of stand is caused by differences in soil, expo- 
sure and density in a restricted locality than by a thousand miles dif- 
ference in location. 



CHAPTER XI 

THE CONSTRUCTION OF STANDARD VOLUME TABLES FOR 
TOTAL CUBIC CONTENTS 

131. Steps in Construction of a Standard Volume Table. The 

steps in the construction of a standard volume table, whether for total 
cubic contents, or for any form of product, are practically the same. 
They are : 

1. Selection of felled trees in sufficient number, and representing 
the complete range of diameter and height classes of the species or 
locality. 

2. Measurement of each tree to secui'c all the data needed for the 
construction of the volume table. 

3. Computation of volume of each tree. 

4. Classification of tree volumes according to diameter and height 
classes. 

5. Averaging the volumes of trees of each separate diameter and 
height class. 

6. Elimination of irregularities in final table by graphic plotting 
and curves. 

132. Selection of Trees for Measurement. As only felled trees 
can be measured with the accuracy needed for construction of volume 
tables, the choice is presented of utilizing timber already felled, either 
by wind, or by loggers, or of felling the trees for measurement. Wind- 
fallen trees are usually of the larger sizes, and scattered individually 
or in groups, and are measured more as a check on rough methods 
of estimating than in the systematic construction of tables. A logging 
job presents the opportunity to secure trees of all diameters except 
those below merchantable size. The operation may be too local in 
extent to embrace the extreme forms desired, and a standard table 
covering the extremes of diameters and complete range of heights 
should be based on trees cut from several different operations covering 
the range of altitude and soil qualities for the species or type. 

The influence of soil, altitude, age and other factors upon the form 
of trees of the same diameter and height class is discussed in Chapter 
XVI. When it can be shown that differences in volume can be cor- 
related with age, or site, separate standard tables may be constructed 
for trees of the specified classes or sites. In this case, the same principle 

154 



THE TREE RECORD 155 

of securing as wide a range of diameter and height classes as possible, 
by distributing the selection of the trees, applies within the limits of 
the predetermined region, type or age class. 

The number of trees necessary to secure a good basis for a volume 
table increases with the range of diameter and height. Ten trees in 
each separate diameter and height class will suffice, and only in a few 
standard tables has this number been secured. This would call for a 
total of 500 to 2500 trees. Ordinarily, a sufficient number of trees 
is easily obtained for the smaller and more common diameter and height 
groups, but the material becomes scarce as the larger sizes are reached. 
The graphic methods of averaging are chiefly useful in overcoming this 
deficiency (§ 138). The use of form factors also facilitates the con- 
struction of tables from fewer trees (§ 175). Standard tables, com- 
puted by averaging the volumes of trees by the method given in this 
chapter should be based on at least 300 trees, and if used as a general 
reference table should never have less than 500 and preferably over 
1000 trees. Local tables based on diameter alone can be made from 
10 to 50 trees. It is desirable to tabulate the number of trees measured 
in each diameter and height class in the field as the work progresses, 
and to make a special effort to find trees of the less numerous sizes to 
fill out the table. On the other hand, the more common sizes should 
be represented by somewhat greater numbers of trees in the table 
than odd sizes, as errors in the table affect the results of estimating 
in proportion to the per cent of volume of the stand which falls in 
the specified classes. 

To secure trees of smaller sizes than are considered merchantable 
by loggers, in order to show total cubic contents for these classes, or 
contents in terms of smaller products not being utilized in that locality, 
the trees may be felled by the mensuration crew. This must be done 
for all sizes in absence of logging, but it adds greatly to the time and 
cost of the work. 

133. The Tree Record. The data for each tree must be entered 
on a separate blank, or printed form, and headed by the items, 

Species, 

Locality, 

Date, 

Name of investigator. 

Number of analysis. 

Records should be carefully filled in with legible figures, using a 

4H or 6H pencil. They constitute permanent records of tree form 

and may be available for use in compiling data many years afterward. 

Description of site factors are useful in determining their influence, 

if any, on the form and volume of trees of the same diameter and height. 



156 CONSTRUCTION OF STANDARD VOLUME TABLES 

These are, 

Soil, origin, whether sedimentary or residual. 

Depth, rock, physical character, sand, etc. 

Exposure and slope. 

Altitude. 

Forest type. 

Character and density of stand. 
These items involve considerable repetition and are often omitted, 
or may be written up for groups of trees. But if the material is to be 
used for investigations, to determine the effect of site factors on form, 
each tree analysis should be associated with a complete description 
covering the points enumerated. 

134. Measurements of the Tree Required for Classification. The 
measurements of the felkxl tree must be taken ])efore the logs are 
removed by skidding. These may be divided according to their pur- 
pose into those needed to 

1. Classify the tree by dimensions and character. 

2. Obtain the volume of the stem and branches. 

The first class of measurements consists of D.B.H., height of stump, 
total height, crown and bole. The D.B.H. (§ 125) is the most important 
measurement taken. This point must be located on the butt log of 
felled trees, unless the D.B.H. has been taken in advance of felling 
the tree. To the stump height is added the additional height needed 
to etjual 4| feet, which is measured upon the butt log. If the butt cut 
is slanting, care is taken to measure from the same point on the log as 
on the stump, thus reproducing the measurement which would be taken 
on the standing tree — otherwise a slight error is incurred. The D.B.H. 
and all other measurements of diameter are taken in two directions, 
at right angles. This is always possible on the felled trees as shown 
in Fig. 25. 

The average of these two diameters is obtained and recorded to 
the nearest ^Vinch, and is never rounded off to the nearest inch. 

The height of stump is taken not only to obtain D.B.H. on felled 
trees, but as a basis from which merchantable length and contents 
is figured (Chapter XII). It is recorded in feet and tenths, or in feet 
and inches. Stump height is measured vertically from the root collar 
or point of contact with the ground, and at the average height of this 
collar. On side hills, this point occm's half way between the upper 
and lower sides of the stump. 

The total height of every tree measured for volume should be recorded, 
whether or not it is to be used as a basis of height classification (§ 137). 
The most accurate method is to stretch a steel tape from the butt to 
tip of crown, along the stem, although a pole graduated in feet is some- 



MEASUREMENTS OF TREE REQUIRED FOR CLASSIFICATION 157 

times substituted. To this height the stump height is added, and the 
total recorded to the nearest foot. The height of a rounded or irregular 
crown is measured to a line drawn at right angles to the bole, and tan- 
gent to the highest point of crown. Height may also be obtained by 
adding together the lengths of the separate sections of the bole, plus 
the distance from the top of last section to tip of trees. 

Character of crown may or may not be required. It is useful in 
hardwoods where separate tree classes may be desired, and in any 
• species where growth is being investigated and as the index of 
form, as indicated 'in Chapter XVI. On felled trees, two measure- 
ments are taken. Width of crown is measured as the tree lies, at 
widest point, at right angles to stem. Length of crown is the dis- 




FiG. 25. — Method of measuring a log twice at right angles to obtain the average 

diameter. 

tance from tip to the point where the lowest vigorous and well-shaped 
green branch joins the bole, or better still, at a point on the bole, oppo- 
site the lower limit of the green crown or foliage. Some judgment is 
required in excluding from crown-length small, feeble or straggling 
single live branches which may have survived by accident on one side 
but do not form part of the main crown of the tree. Dead branches 
or knots form no part of the crown. 

The position or class of the crown in the stand may also be described, 
as open-grown, dominant, co-dominant, intermediate, or overtopped. 
This is best judged before felling. 

The following definitions have been adopted as standard by the Society of 
American Foresters. 

Crown Class. All trees in a stand occupying a similar position in the crown 
cxyver. The crown classes usually distinguished are: 



158 CONSTRUCTION OF STANDARD VOLUME TABLES 

Dominant. Trees with crowns extending above the general level of the forest 
canopy and receiving full light from above and partly from the side; larger than 
the average trees in the stand, and with crowns well developed but possibly some- 
what crowded on the sides. 

Co-dominant . Trees with crowns forming the general level of the forest canopy 
and receiving full light from above but comparatively Httle from the sides; usually 
with medium-sized crowns more or less crowded on the sides. 

Intermediate. Trees with crowns below, but still extending into the general 
level of the forest canopy, receiving a little direct light from above, but 
none from the sides; usually with small crowns considerably crowded on the 
sides. 

Overtopped. Trees with crowns entirely below the general forest 'canopy and 
receiving no direct light either from above or from the sides. These may be 
further divided into oppressed, usually with small, poorly developed crowns, still 
alive, and possibly able to recover; and suppressed or dying and dead. 

As currently used, overtopped trees are now classed as suppressed; and an 
additional class, open-grown, is added, consisting of trees standing alone with 
crown free on all sides. 

The hole is not described unless there is some marked peculiarity 
which may explain an abnormal shape or volume and enable the investi- 
gator later to decide whether to use or reject it in his tables. Such 
peculiarities include forks, dead tops, abnormal or swollen butts, especi- 
ally if the D.B.H. is affected, or other deformities in shape. The pres- 
ence of rot, shake, or other internal defects may be noted, but does 
not influence the subsequent measurements (§ 156) or volume of the 
tree, unless its form is affected abnormally, as sometimes happens 
when rot at the butt causes abnormal butt swelling extending beyond 
D.B.H. 

135. Measurements Required to Obtain the Volume of the Tree. 
Systems Used. While the object of measurements of the stem is to 
obtain its volume, these also serve to record the form of the bole. The 
diameter is taken (§ 29) at definite points, dividing the bole into lengths 
which are recorded consecutively. The cubic volume of round logs 
of any length is easily computed from the end diameters (Smalian 
formula) if the proper precautions are taken to guard against the influ- 
ence of butt swelling (§ 29). But if the recorded diameters or form 
of the trees are to be used to get average form or taper (§ 166) as well 
as merely for volume, these measurements should be taken at the same 
heights or intervals on all trees. 

For cubic volume, the log lengths into which the bole is cut by the 
loggers may be disregarded. This factor would exert no appreciable 
influence on the tree contents when the full volume of each log is accu- 
rately obtained. 

There are three systems of taking these upper diameter or taper 
measurements, as follows (Fig. 30, § 155) : 



VOLUME OF THE TREE. SYSTEMS USED 159 

System A. Disregard stump height. Take diameter at every 
10 feet from ground to tip. Record length of tip above last 10-foot 
taper. 

This method permits of accurate averaging of these diameters on 
different trees to obtain average form, and also gives the total cubic 
volume of the tree. But it is unsafe to rely solely upon these measure- 
ments for the volume of the first 10-foot log, which should be supple- 
mented by stump taper measurements, taken at 1, 2, 3, 4 and 4| feet 
from the ground. This gives a complete record of form and an accu- 
rate basis for total volume. 

By means of form or taper tables (§ 167) based on these measure- 
ments, the diameters at any other points may be obtained from dia- 
grams, and the volume of the tree can then be calculated for any unit 
of product. 

System B. This method is a compromise between measurements 
intended solely to secure form or total cubic volume, and those required 
for merchantable volume (§ 145). The height of stump is first recorded 
and the height of upper diameters is then taken from the stump as a 
base. As stump height tends to increase with diameter of tree, the 
upper measurements of larger trees fall at higher points on the bole, 
by just the difference in stump heights. This inaccuracy is usually 
accepted and the diameters which fall at equal height above the stump 
are averaged together. 

The length of log or interval adopted for upper diameter or taper 
measurements by this method is a multiple of 4 feet. Four-foot inter- 
vals give closest results, and correspond to cordwood lengths. A more 
common interval is 8 feet, corresponding with the standard length of 
cross-ties. Greater lengths give less accurate permanent data. If 
only the 16-foot tapers are required for the immediate purpose of the 
table, it is comparatively little extra work to take the 8-foot points 
as well, for future use if needed. 

System C. By this method the logs as cut by the sawyers are 
measured as they lie, for diameter and length. As these commercial 
lengths vary, the taper measurements for different trees will fall at 
several different points even for the first log, and require tabulation 
at 2-foot intervals. Except when measured for total cubic feet, the 
resultant, volumes will vary according to the lengths cut (§43), and 
not solely according to the dimensions of the tree as by Systems A 
and B. No advantage is gained by the securing of volume correspond- 
ing to the used lengths of the tree measured, since in every logging 
job, the average of lengths used will differ. This method is therefore 
inadvisable. But a record can be made on the analysis blank of the 
log lengths actually cut, and their scaled contents, to determine the 



160 



CONSTRUCTION OF STANDARD VOLUME TABLES 



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COMPUTATION OF VOLUME OF THE TREE 161 

difference between volumes as cut and scaled, and volumes from regular 
tapers. 

In case the study of the growth of trees at upper sections is required 
(§ 289) either the trees will have to be felled and bucked into sections 
of even lengths by System A or System B, or else the logs as cut by 
System C must be accepted as the basis of this growth study. 

For total cubic volume, the taper measurements are continued 
to the tip in either system. With slight additional cost, these extra 
measurements taken above the merchantable top diameter limit com- 
plete a permanent record of tree form available for future computa- 
tion of volume for any unit or limit of merchantable sizes. 

A further modification is the addition of trimming lengths, usually 
standardized as yV^eet in 16 feet, so that the points marked fall at 
8.15 feet, 16.3 feet, 24.45 feet, etc. If this is done the fact should be 
be noted on the analysis. Total cubic volume is obtained as accurately 
by this method as by System A, and in addition, the data can be used 
directly to determine the volume in board feet. It is therefore pref- 
erable for most objects to System A. 

The width, single, of bark is measured at each diameter (§ 29), and 
recorded as read. This width is then doubled and subtracted to 
obtain diameter inside bark.^ 

If the volume of sapwood is desired, this will require the sectioning 
of the tree, and measurement of width of sap. Sapwood volume is 
therefore most easily obtained by System C. 

The measurements are entered on a blank, of which an example 
is .shown on p. 160. 

This completes the field recoi-d. The remainder of the work is 
performed at any time in the office. 

The crew for field measurements of volume, when the trees are 
already felled, should consist of two to three men, one of whom records 
the data while the others measure the tree. 

136. Computation of Volume of the Tree. For total cubic volume, 
each section is usually computed by the Smalian or mean end formula 
in which 

B = area of large end of section in square feet; 

6 = area of small end of section in square feet; 

? = length of section in feet; 

y=^ cubic volume. 

1 Abbreviations are used, as follows : 

Diameter outside bark, D.O.B. 
Diameter inside bark, D.I.B. 



162 CONSTRUCTION OF STANDARD VOLUME TABLES 

Then 

For the sum of the volumes of the sections each end area except 
the first and last is evidently used twice. A series of three such sec- 
tions would total 



y= 



m^^^-^H^y- 



When, as in systems A and B, equal lengths of section (/) are used, 
the formula can be expressed 

i.e., average the first and last basal areas, and add the remaining areas. 
Then multiply by length of one section to obtain the sum of volumes 
of the sections. 

The areas in square feet, corresponding to the diameters of each 
section are found in Table LXXVIII, Appendix C, p. 490. 

Sections different in length from the standard must be computed 
separately. 

The tip, beyond the last taper, is computed as a paraboloid, by the 
same formula. 

The volume of stump, needed to complete the tree when system B 
is used, is standardized by custom as a cylinder, whose diameter is that 
of the stump section, thus neglecting the variable factor of stump 
taper. Its volume is therefore 

V^Bl. 

System A permits the volume of the section up to 4 or 4| feet to be 
computed accurately if desired. 

Owing to the serious error incurred by measuring the butt section 
by the Smalian method, the use of Ruber's formula for the first 8- or 
16-foot log may give more consistent results. In this case, for a 16- 
foot log (/) the basal area at 8 feet (6') gives the log volume, or 

V = h'l. 

A check should be made by this method against the Smalian method 
for the butt section (§ 29). 

The total cubic volume of branches and twigs is practically never 



CLASSIFICATION AND AVERAGING OF TREE VOLUMES 163 

computed. The measurement of merchantable volume of hmbs and 
branches is discussed in § 146. 

For obtaining the total volume of the tree bole exclusive of branches 
by regarding the bole as a complete paraboloid, the so-called Schiffel's 
Formula may be applied. For this purpose the area of the cross 
section at D.B.H., and one at one-haK height above stump is obtained 
and applied, thus: 

V=(.16B-\-Mbi)h (§177). 

Volume of Bark. The volume of the tree may be computed from 
D.O.B. to give total cubic contents with bark. It is then computed, 
if necessary, from the D.I.B., to give the peeled contents or wood 
without bark. The volume of bark is obtained by subtraction of the 
second from the first result. 

Volume tables give the volume with bark, or without bark, accord- 
ing to the use to which wood is put and the form in which it is sold. 
When the peeled volumes are given, the per cent of bark in terms of 
peeled volume may be shown for each diameter. 

137. Classification and Averaging of Tree Volumes According to 
Diameter and Height Classes. 1. The separate sheets are now sorted 
first into diameter classes (§ 127). 

2. The height classes, for tables giving total cubic volume, are based 
on total height of tree. Whether 10-foot, or 5-foot classes are used 
depends on the total height of the species. For second-growth hard- 
woods or small timber, 5-foot classes are preferred, while in the extremely 
tall timber of the West Coast, 20-foot classes are sometimes sufficient. 
For either standard, trees are placed nearest their actual height. The 
trees of each diameter class are now sorted into their respective height 
classes. The trees in each separate diameter and height class are then 
checked to see that no mistakes of classification have been made. 

3. The average volume is found for the trees of each separate group 
or class comprising all trees falling in the same diameter and height 
class. 

If trees having the same diameter and height had similar forms, 
the volumes of all trees in any one diameter and height class would 
be equal, except for the differences due to the fact that the actual 
diameter, or height, though falling within the size limits required, may 
be larger or smaller than the exact standard size of the class. 

But variation in the form of the bole is a third factor which causes 
considerable variation in volume for trees of the same total height 
and diameter (§ 166). Trees whose form is full, lying between the 
paraboloid and the cylinder, have a correspondingly greater volume 
than trees with a form lying between the paraboloid and cone, or neUoid 



164 



CONSTRUCTION OF STANDARD VOLUME TABLES 



(§ 26), The extreme range of volume caused by differences of form 
alone for trees of the same height and D.B.H. is as much as 40 per cent. 
Even the average volume of trees of the same ages or sites may differ 
by more than 20 per cent. 

The volume of single trees follow the general law of averages. 
Those which depart most widely from this law are few in number, 
while a range of 5 per cent above or below the average would probably 
include by far the larger number of trees in fairly uniform stands. 

When the exact volume of a specific tree is wanted it is unsafe to 
assume that this tree is an average specimen. It must be measured 
separately. But in estimating standing timber, the object sought is the 
total volume of the stand, or the sum of all trees. If the average vol- 
ume of trees of each size class is correctly given in a volume table, 
the cruiser can assume that every tree tallied is an average tree, and 
the result or total will be the same as if the true volume of each sepa- 
rate tree were measured. 

This averaging of the variable individual volumes of trees of each 
class to obtain a reliable average volume is the principal service rendered 
by volume tables. The timber cruiser stretches this same principle 
much farther when he attempts to average the volumes of trees of totally 
different diameters and heights, and the chances for error are much 
greater, especially as this is usually a mental process or guess, while 
the averaging of trees in a volume table is a calculation based on exact 
measurements. 

The method of obtaining the average volume of trees for a given 
size is as follows. Enter on a sheet, labeled with the diameter and height 
class, the data for each tree, according to the illustration given below 
for four trees. Place at top of sheet the tree class, e.g., 



13 Inches — 60 Feet 


Diameter. 
Inches 


Height. 
Feet 


Volume with bark. 
Cubic feet 


12.7 
13.1 
13.4 
13.4 


56 
58 
61 
62 

257 
59.25 


59.0 
63.2 
66.0 

68.2 

256.4 

64.1 

■ 


4)52.6 
13.15 



CLASSIFICATION AND AVERAGING OF TREE VOLUMES 165 



TABLE XXVII 

Preliminary Averages for Pitch Pine. Volume Table Based on 

Diameter and Total Height. 139 Trees 

Height Classes — -Feet 





D.B.H. 

Inches 

7 


50 


55 


60 


65 


70 


75 


80 






7.5 1 
6.96 
52.6 














8 


8.0 1 
8.73 
52.0 
















9 








9.0 1 
14.28 
63.0 










10 


10.2 1 
12.51 
50.0 


9.75 4 
14.88 
53.4 


10.0 1 
17.37 
58.1 


10.5 2 
19.05 
65.8 










11 


11.5 1 
17.78 
50.0 


10.9 6 
17.67 
55.6 


11.1 3 
19.78 
59.35 


11.1 2 
23.35 
63.2 










12 


12.3 1 
17.93 
52.0 


12.3 6 
24.18 
55.1 


12.2 8 
24.27 
59.6 


12.0 1 
26.09 
63.0 








Legend 


13 


12.9 4 
23.4 
49.6 


13.1 11 
26.23 
54.2 


13.15 4 
27.53 
59.25 


13.4 2 
34.27 
65.0 








D.B.H. No. 
Inches Trees 


14 




13.9 6 
31.8 
56.6 


14.0 9 
31.61 
60.3 


14.1 5 
34.05 
64.1 


14.1 2 
42.32 
68.5 


13.6 1 
38.92 
73.4 


14.3 1 
46.1 
78.0 


Cubic 
feet 


15 


14.7 2 
32.9 
51.5 


15.1 1 
36.1 
57.0 


15.1 3 
39.44 
60.2 


15.2 4 
39.96 
64.2 


15.1 2 
45.3 

68.8 


15.0 1 
43.55 
77.0 




Total 

Height 

Feet 


16 




16.3 2 
37.15 
54.5 


16.1 7 
43.71 
59.8 


15.9 3 
44.69 
64.9 


16.1 5 
49.21 
69.3 








17 




16.9 3 
44.67 
54.8 


16.7 2 
47.26 
60.0 


16.8 2 
47.82 
64.8 


17.1 1 
51.3 
68.0 


17.1 2 
55.67 
73.45 


17.0 1 
65.14 
78.0 




18 






18.0 1 
54.82 
60.0 


18.0 4 
61.57 
64.25 


18.3 2 
59.25 
68.1 








19 








18.6 1 
60.45 
66.0 


19.1 3 
65.27 
70.2 


19.0 2 
71.82 
74.0 






20 










20.0 1 
69.56 
67.8 







166 CONSTRUCTION OF STANDARD VOLUME TABLES 

The quotients represent respectively the actual average diameter, 
height and volume for the class. These data, together with the number 
of trees measured in each class, are entered on a large sheet in the form 
shown in Table XXVII, p. 165, and constitute the basic or rough table 
which is the first step in preparing a standard volume table. Thus 
64.1 cubic feet is not the average volume for 13-inch trees 60 feet high 
but for trees averaging 13.15 inches and 59.25 feet in height. 

138. The Graphic Plotting of Data — Its Advantages. The volumes shown in 
such a table should increase with both diameter and height. If sufficient basic 
data has been obtained, this rate of increase in the values of the table, both verti- 
cally and horizontally, will follow the law of averages which expresses the true 
relation of the two variables; for the vertical columns, volume and diameter; for 
the horizontal, volume and height. But where only a few trees are obtained in a 
class, these trees may not only be larger or smaller in diameter and height than the 
true average, but may have too full or too slender a form, and the average of their 
volumes will be correspondingly higher or lower than the regular progression to be 
expected. The form of this progression or increase will be determined by the 
character of the two variables. For cubic volume based on diameter, with trees 
of the same height and form, the increase in volume will be proportional to D"^. 
If these values are plotted on cross-section paper, the result will be a curve showing 
graphically to the eye the law of increase in volume based on diameter. 

The increase in volume based on height can be shown in a similar manner by 
plotting the volumes and heights. This curve will differ in shape from the first, 
since volume tends to increase directly as height for trees of the same diameter, 
and the curve showing this approaches a straight line. When thus presented to 
the eye, any irregularities or inconsistencies in the average volumes obtained in 
Table XXVII become evident at once, while to detect them by mere examination 
or checking of the arithmetical table would be far from satisfactory. 

Since such irregular values do not conform to the general law of increase in 
volume based on diameter and height, they cannot be depended upon to give the 
true average volume of all the trees of a size class. One of two things must now 
be done — either more data must be collected in the field in order to improve these 
averages, or the averages obtained must be harmonized, and these irregular values 
changed or corrected. The irregular volumes plotted would be based on sufficient 
field data to bring out the real tendency or character of the law of the relations 
sought. The minor irregularities in this case are not serious enough to prevent a 
fairly accurate approximation of this law and a drawing of the curve as indicated 
by the data. 

The principles of graphic plotting are treated in analytical geometry, or graphic 
algebra. The relation of the two variable quantities is shown by a series of plotted 
points in which the horizontal and vertical lines each represent a scale of values 
corresponding to one of the quantities or variables. Both being positive quantities, 
the lower left-hand corner of the chart is taken as zero, or the origin. The hori- 
zontal line passing through this point along the base of the sheet is the axis of 
abscissa; or horizontal scale, and the abscissa or value of each point is measured 
parallel with this axis or along the scale thus indicated. The vertical line through 
the origin, forming the left margin of sheet is the axis of ordinates or vertical scale. 
The zero, or intersection of these two axes, is usually located to the right and above 
the extreme lower corner of the sheet to give a margin for entering the scales. The 



THE GRAPHIC PLOTTING OF DATA 



167 



scale of diameters, by inches, is then placed along the horizontal scale while the 
volume scale is entered on the vertical scale. The whole forms a system of rectan- 
gular co-ordinates. Each point on the paper represents two quantities, a diameter, 
measured parallel with the base, and forming the abscissa of the point, and a 
volume, measured vertically, and forming an ordinate. This is illustrated by 
Fig. 26. 

In this figure, the volumes of three average trees, or the averages volumes of 
three groups of trees have been plotted, namely, 10-inch, 13.15-inch and 16.1-inch 
trees. The horizontal and vertical values of each point are indicated by dotted 
lines. If the theoretical 
relation of volume, and 
diameter for all points 
is as y to p.r- we would 
not only expect y (vol- 
ume) to increase faster 
than X (diameter), but 
this increase would be 
in the form of a regular 
curve, and once the 
position of this curve 
is indicated by a suffi- 
cient number of reli- 
able points, all other 
values for x and y, 
representing the vol- 
umes for all diameters, 
would fall on the same 
curve. False or ab- 
normal average vol- 
umes obtained from 
too few trees will not 
fall exactly on the 

curve, but above or below it. The greater the number of trees used in obtain- 
ing an average point, the more closely will the point representing this value approach 
or coincide with the curve. 

The actual shape of the curve will depend upon the relation arbitrarily estab- 
lished between the two scales. Doubling the values on the ordinates, for instance, 
reduces the ordinate distance one-half. The scale selected must bring all values 
within the boundaries of the sheet, which is usually accomplished if the largest 
ordinate is not less than one-half nor greater than one and one-half times the 
greatest abscissa. 

The value of using this method is that each separate point or average aids in 
establishing the law, or fixing the values for all the others. If enough good or 
well-weighted points are obtained, they correct the abnormahty of other points 
based on insufficient data and even show up arithmetical mistakes in obtaining 
these averages. The curve makes possible the interpretation of missing data, but 
it is considered unsafe to extend it to cover values beyond the limits of the original 
data. 

Although from the standpoint of mathematics it makes no difference which 
variable is plotted on the horizontal and which on the vertical scale, yet as the 
purpose of this plotting is to convey to the eye the tendency or law of increase in 



*3 






















/ 




x 










Abscissa IC. 


L 








Y ■ 




o 
40 

35 

S30 

Id 
•I 25 

220 






















/ 






















■/ 




















^ 
<^y 


f 














Atsc 


ssal3 


15" 




V 






1 














^/ 


I 
















r 














Absci 


..sa 10 




^ 




o 






9 






10 

5 

X 








^ 












5 




Ti 


1 
1 




3 

a 














i 




sS 






o 














.a 
o 




O 


1 











10 11 12 13 
Axis of Abscissae 



11 15 16 Inches of D.B.H. 



Fig. 26. — Rectangular coordinates, showing position of 
a curve of volume on diameter as determined by three 
points whose ordinates and abscissae are known. 



168 



CONSTRUCTION OF STANDARD VOLUME TABLES 



one variable when based upon another definite variable, as for instance, the increase 
in volume due to increase in diameter by 1-inch classes, it is always preferable to 
plot the independent variables on the horizontal scale and the dependent variables 
on the vertical scale. 

Neglect of this precaution not only conveys an ocular impression the reverse of 
the actual law, but tends to create the false notion that the two variables are inter- 
changeable, whereas one must always be an independent or fixed base, on which 




10 11 12 13 14 15 16 17 18 19 

D.B.H. Inches 

Fig. 27. — Curve of volume based on D.B.H. for trees of a single height class. 

the required data are collected, classified and arranged. For instance, in deter- 
mining the relation between D.B.H. and age of trees, absolutely different results 
are obtained if in the first instance, . the average D.B.H. is found for all trees of 
given age classes, and in the second, the average age is determined for all trees of 
given D.B.H. classes (§ 275). The values of these tables or curves are not inter- 
changeable. The dependent variable can always be identified as the one whose 
values are sought; the independent, the one whose values are already known. 

The use of curves, or graphic plotting, enables the investigator to obtain a 
given degree of accuracy with a greatly reduced number of field measurements. 



APPLICATION OF GRAPHIC METHOD 169 

This saving in field work is from 100 to 500 per cent; in fact it would be impractical, 
though possible, to get the same degree of accuracy by the averaging of field data 
as in Table XXVII without using the graphic method. The application of these 
principles would have greatly improved the construction of certain log rules, 
notably the Scribner rule ( § 68) . 

139. Application of Graphic Method in Constructing Volume Tables. — In 
applying this method to the values in Table XXVII volume is evidently the variable 
whose value is sought, while diameter and height are the two independent variables. 
It is evident that not more than two values can be plotted in a single point, 
nor more than two variables, as for instance, diameters and volumes in a single 
curve. The volume of trees varies with both diameter and height, yet variations 
due to height cannot be shown in the same curve with those due to diameter. But 
if we select from the original table (XXVII) the volume of trees, all of which fall 
in the same height class, the factor of height, for these volumes, becomes a constant, 
except for deviations from the true average height of the class, which can be ignored 
in plotting this curve. The curve formed by the volumes of this group of selected 
trees will be designated as the volume curve based on diameters, for trees of the 
specified height. Such a curve is shown in Fig. 27, with the original average volumes 
plotted. 

In determining just where the curve should fall, the weight of each point is 
influenced by the number of trees included in the average column for that diameter; 
the weight of a point varies with the square root of the number of entries and not 
directly with the number of entries. Thus an average of a point representing one 
tree and a point representing four trees would be on a straight line connecting them 
and one-third of the way from the "4" point to the "1" point. The number of 
trees in each class should therefore be entered on the sheets opposite the point 
representing the volume. 

The original -volume for the trees of a given diameter class may represent a 
diameter slightly larger or smaller than the exact inch. For instance, in Table 
XXVII, the average diameter for 17-inch trees, 55 feet high, was 16.7 inches. This 
volume should not be entered above 17 inches, but above its true average diameter. 

When the curve is completed, the values are read from it for each e.xact inch of 
diameter. 

A comparison of the original and harmonized values from the above curve is given 
in Table XXVIII, p. 171. 

The averages for 33 out of 38 trees and 6 out of 9 diameter classes fall within 
2 per cent of the curve. 

140. Harmonized Curves for Standard Volume Tables Based on 
Diameter. So far, the volumes of trees of different diameters for but 
one height class have been shown. By the same method, a curve is 
constructed for each separate height class, based on the scale of diam- 
eters. If, instead of making each of these curves on separate sheets, 
they are all placed on the same sheet, their relation to each other is 
shown.^ All curves should show the same general trend, in harmony 
with the law of variation between diameter and volume. The set 

• Where insufficient data are available and height divisions are small, the values 
for different heights will frequently overlap. In such cases it is better to plot 
every alternate height class first, and draw the respective curves befoi'e plotting the 
intervening classes. 



170 



CONSTRUCTION OF STANDARD VOLUME TABLES 



of harmonized curves of volume based on diameter is shown in Fig. 
28 with height class of the trees in each curve indicated. 

From this set of curves a table can be read, whose form is similar 
to that of Table XXVII, but whose volumes increase regularly with 




14 15 16 

Diameter, Itiches 

Fig. 28. — Curves of volume based on diameter for separate height classes, plotted 
from original averages in Table XXVII. 



diameter, and whose values are interpolated to even inch classes from 
the averages of the original table. 

141. Harmonized Curves Based on Heights. But this table is 
not necessarily in final form, for the variations caused by height must 
also be harmonized. The first set of values has been made regular 



HARMONIZED CURVES BASED ON HEIGHTS 



171 



TABLE XXVIII 

Comparison of Original and Harmonized Average Volumes 



D. B. H. 


Original 


Harmonized 






volumes. 


volumes. 


Remarks 


Inches 


Cubic feet 


Cubic feet 




9 




14.0 




10 


17.38 


16.5 


One tree with full bole 


11 


19.78 


19.75 




12 


24.27 


23.4 




13 


27.53 


27.4 




14 


31 61 


32.1 




15 


39.44 


37.3 


Original volumes evidently too cylin- 
drical for average 


16 


43.71 


43.1 




17 


47.26 


49.5 


Original diameter 16.7 inches, but aver- 
age volume 


18 


54.82 


56.2 


One tree with poor form 


19 




63.6 





TABLE XXIX 

Volumes Read from Curves of Volume on Diameter for Different Height 

Classes 









Height Classes 


, Feet 






D. B. H. 


50 


55 


60 


65 


70 


75 


80 


Inches 






Cubic Fee 


r, 






9 


9.5 


12.2 


13.0 


14.0 








10 


12.9 


15.4 


16.5 


17.6 








11 


16.2 


18.8 


19.9 


21.3 








12 


19.7 


22.4 


23.2 


25.1 








13 


23.5 


26.2 


27.1 


29.4 








14 


27.8 


30.6 


31.8 


34.1 


39.3 


41.0 


45.7 


15 


32.3 


35.0 


37.1 


39.0 


44.0 


46.0 


51.4 


16 




40.0 


43.0 


44.7 


49.0 


51.5 


57.2 


17 




45.0 


49.2 


51.3 


54.4 


57.4 


63.6 


18 






55.5 


58.0 


60.0 


63.8 


70.2 


19 








65.0 


66.0 


70.2 




20 

















172 CONSTRUCTION OF STANDARD VOLUME TABLES 

within each height class separately, but this does not prevent the values 
of all the trees of a given height class from being too low or too high. 
In fact, if one of the volume curves representing a height class is incor- 
rectly drawn lower or higher than it should be, this very result is pro- 
duced.^ 

The law of variation of volume based on height may be expressed 
by the equation y = px, since volume (y) increases approximately in 
direct proportion to height (x). For trees of the same diameter, whose 
volumes lie on the same ordinate in Fig. 28, the curves of volumes for 
regular gradations of height should be spaced at about equal distances. 
This interval, of course, increases with each diameter class. Since this 
is known, the first set of curves based on diameter may be harmonized, 
not only in direction but in spacing, being placed at equal intervals 
on each successive ordinate. The resultant table will then show volumes 
increasing regularly by height. 

A still better method of securing this regularity is to plot, from the 
values obtained from the first set of curves, a second set in which 
heights are the determinate variable, or basis plotted on the horizontal 
scale, and volumes are plotted vertically as before. Diameter must 
now be eliminated as a variable, by plotting all the volumes for trees 
of a single diameter class in the same curve. Beginning with the first 
diameter class in Fig. 28, which is intersected by two or more curves 
of volume representing different height classes, these volumes at the 
intersecting points are read, beginning with the lowest. The series 
of values thus obtained represents the volumes of successive height 
classes, and as such are plotted on the new sheet, and connected to 
form a new curve, which represents only trees of the diameter class 
so taken. 

Each point so plotted should be placed above the actual average 
height for the class, as found in the original averages shown in Table 
XXVII, e.g., for the 15-inch curve, the 55-foot class must be plotted, 
not above 55 feet, but above 57 feet, which is the actual average 
height for this class. 

Separate new curves are thus plotted for the trees in each diameter 
class. Instead of plotting these values direct from the first set of 
curves, a table may be made from the values read from these curves, 

1 The tendency to error may be greatly reduced in the original curves if the 
the square of the diameter is made the basis of the table, or abscisssE scale, in which 
case the curves take the form of straight lines characteristic of those based on 
height. The same result may be obtained by plotting on logarithmic cross-section 
paper. (Logarithmic Cross-section Paper in Forest Mensuration, Donald Bruce, 
Journal of Forestry, Vol. XV, 1917, p, 335.) 



HARMONIZED CURVES BASED ON HEIGHTS 



173 



and the new values then replotted from this table. In this case, the 
values from each curve will be read horizontally from the table instead 
of from the vertical 
column as in the first 
instance. 

"Strip" Method of 
Re-plotting. A rapid 
method of replotting 
direct from the curve is 
by means of a strip of 
paper. The zero or end 
of strip is placed on the 
base or abscissa, and 
held in a vertical posi- 
tion, so that the edge 
lies on the ordinate re- 
presenting the diameter 
class to be transferred; 
a mark is then made 
where the curve of vol- 
ume for each successive 
height class intersects 
the strip. These marks 
may be numbered or 
otherwise designated, 
but their mere order is 
a sufficient identifica- 
tion. Transferring this 
paper to the second 
sheet, the vertical or 
ordinate distance (which 
represents volume in 
each set of curves) for 
the first height class, 
is plotted on the ordi- 
nate intersecting the 
abscissa representing 
that height. The strip 
is then moved to the 
right, to intersect the 
next height on the scale 
and the corresponding 
volume point transferred 

to the sheet. When plotted thus, these volumes indicate the position of the 
curve of volume for different heights, for trees of the given diameter class. i 




60 65 70 
Height. Fee* 

Fig. 29. — Curves of volume based on height. Original 
curves, dotted, from curves shown in Fig. 28, or 
values from Table XXIX. Harmonized curves 
drawn. 



iThis method is described by W. B. Barrows, "Reading and Replotting Curves 
by the Strip Method," Proc. Soc. Am. Foresters, Vol. X, 1915, p. 65. 



174 



CONSTRUCTION OF STANDARD VOLUME TABLES 



Irregularities in spacing the first set of curves are now shown by 
this second set as similar distortions of each curve where they inter- 
sect the same ordinate. This is shown in Fig. 29.^ 

Volumes read from this second and final set of curves increase with 
both diameter and height according to the true laws of variation appli- 
cable to each dimension. In this way Standard Volume Tables are 
secured, which may be applied to a species throughout its range, unless 
it is convincingly shown that there are consistent differences in form 
and volume not due to either height or diameter, which can be cor- 
related with age or site, and call for separate standard table. 

TABLE XXX 

Standard Volume Table Read from Curves of Volume on Height for 
Different Diameter Classes 





Height Classes, Feet 


D.B.H. 


50 


55 


60 


65 


70 


75 


80 


Inches 


Cubic Feet 


9 


10.3 


11.8 


13.2 


14.6 








10 


13.6 


15.1 


16.6 


18.1 








11 


17.0 


18.5 


20.0 


21.5 








12 


20.2 


22.1 


24.0 


26.0 








13 


24.0 


26.2 


28.4 


30.6 








14 


28.0 


30.6 


33.2 


35.9 


38.5 


41.2 


43.8 


15 


32.4 


35.2 


38.0 


40.8 


43.6 


46.4 


49.2 


16 




40.0 


43.0 


46.0 


49.0 


52.0 


55.0 


17 




45.4 


48.6 


51.8 


54.9 


58.0 


61.1 


18 






55.3 


58.3 


61.2 


64.2 


67.1 


19 






61.2 


64.4 


67.6 


70.8 


74.0 



142. Local Volume Tables — Their Construction and Use. In the 
absence of a standard table, or when for any reason the available tables 
are not reliable and there is no time to construct a table for all heights 

1 Based on the law of variation between volume and height, this set of curves 
(in rectangular co-ordinates the term "curve" applies to any line, curved or straight, 
which follows a regular law and can be expressed by a formula) consists of lines which 
are nearly straight, but not parallel, since the difference in volume increases with, 
^ach diameter class representing a single curve. 



LOCAL VOLUME TABLES 



175 



and diameters, a local table based on diameter alone may be made 
directly, from whatever number of measurements can be secured. The 
volumes of all trees of the same diameter are averaged regardless of 
height. These averages must then be plotted, and a single curve drawn 
similar to that shown in Fig. 27 but containing trees of all heights. 
From this curve average volumes for each diameter class are read. 

When diameter is shown in the table, such tables are useful only 
within the same stand, age class or site class in which they are con- 
structed. Timber whose average height is greater or smaller, for any 
cause, for trees of the same diameter classes, cannot be measured by 
this local table but require a new basis of volumes. If it is found that 
the heights do average the same for each diameter the local table can 
be used unless it is known that other factors influence form sufficiently 
to require its correction. But where no record is made of heights of 
the trees used in constructing the table, as frequently happens, the 
cruiser has no way of knowing whether the table applies to any stand 
but that in which it was made. Where it is expected that such local 
tables may be used again, heights should be measured as well as diam- 
eter, and a curve of height on diameter drawn. The full data for such 
a local table, which is to be saved for possible future use, are: 



TABLE XXXI 
Local Volume Table, Form 



D. B. H. 


Volume. 


Height. 


Inches 


Cubic feet 


Feet 


12 


20.2 


50 


13 


25.3 


53 


14 


32.1 


58 


15 


39.1 


62 


16 


46.0 


65 


etc. 







143. The Derivation of Local Volume Tables from Standard Tables, 

Where a reliable standard volume table is available, it is not necessary 
to construct a local volume table based solely on diameter. If the 
estimator does not need or desire to distinguish different heights in 
tallying trees, he may select the volumes from the standard table which 
represent trees of the average heights of the given stand, and tally 
diameter only. 

The first step is to determine the average height of trees of each 
diameter class, by means of a few measurements, and the plotting of 



176 CONSTRUCTION OF STANDARD VOLUME TABLES 

a curve to show the average height of trees of each diameter (§ 209). 
The volumes corresponding to these heights in the standard table are 
taken. When the height for a diameter class falls between the fixed 
heights given in the table, the volume for this class must be interpolated. 
For instance, a height of 54 feet in a table showing volumes for 50- 
and 60-foot trees, would require an addition to the 50-foot volume, 
of four-tenths of the difference between those of the 50- and 60-foot 
classes. 

The standard volume table therefore permanently replaces all local 
tables, provided the average form, the unit of volume, and the merchant- 
able units used correspond to the conditions for the timber to be meas- 
ured (§ 205). 

144. Volume Tables for Peeled or Solid-Wood Contents. To 
obtain volume tables for solid or peeled contents, the original tree 
volumes are computed from D.I.B. measurements taken at stump and 
at each section. The D.B.H. of each tree is based on the measurement 
outside bark just as for volume tables with bark. This permits the 
comparison of the volumes with and without bark for trees of the same 
size class. 

References 

Volume Tables and the Bases on Which They May Be Built, Judson F. Clark, 

Forestry Quarterly. Vol. I, 1903, p. 6 (Schiffel's formula). 
Volume Tables, Henry S. Graves, Forestry Quarterly, Vol. Ill, 1905, p. 227. 



CHAPTER XII 

STANDARD VOLUME TABLES FOR MERCHANTABLE CUBIC 
VOLUME AND CORDS 

145. Purpose and Derivation of Tables for Cubic Volume of Trees. 

Volume tables for merchantable cubic volume are intended to measure 
the merchantable portion of trees, thus excluding the stump, top and 
branches too small for use. In America these tables are used for the 
measurement of firewood, pulp or acid wood, or products to be totally 
consumed or disintegrated (§ 18). The volumes in this class of tables 
may be obtained from those for total cubic volume by subtracting 
the waste or unused portion of the stem represented by stump and 
top, or the merchantable portion of the bole may be computed directly. 
For board contents or other units, different tables are employed. 

146. Branch-wood or Lapwood. Where branch-wood is of sufficient 
size for use, which occurs with many hardwoods used for firewood, its 
volume is computed separately from the stem, usually in 4-foot lengths, 
each of which is calipered at the center of the stick (by Huber's formula) . 
The additional volume of branches is termed lapwood. The better 
method is to keep this volume separate from that of the main bole 
in the volume table, and express it by diameter classes as a per cent 
to be added to the volumes in the table. Lapwood is an exceedingly 
variable quantity, chiefly found in hardwoods, practically absent in 
conifers, and dependent entirely upon the degree of density of the stand, 
which also affects the form of the bole itself. Where lapwood is included 
with the volume of the bole, the trees should be separated not only by 
diameter but by crown classes, dependent on the degree of crowding 
and the relative spread of crowns. No more than three such classes 
would be practical, namely open-grown or large spreading crowns 
containing a large per cent of merchantable lapwood, medium crowns 
containing an appreciable quantity of lapwood, and trees without 
lapwood in quantity sufficient to affect the estimates. 

Standard volume tables (§140) will seldom include lapwood but will 
be confined to the volume of the main stem. Where lapwood is included, 
the tables will usually be local in character, and based solely on diam- 
eter, with a separate table for each crown class. 

147. Merchantable Limit in Tops and at D.B.H. Where cubic 
volume is utilized; the limit of merchantable size in the tops lies between 

177 



178 STANDARD VOLUME TABLES 

2 and 3 inches, outside bark. The same standard apphes to branches. 
The " merchantable " top diameter for European conifers is about 7 
centimeters or 3 inches outside bark, but this apphes to wood for manu- 
facture, and practically the whole tree may be taken by the use of fagots ; 
i.e., brushwood, done up in bundles. There is considerable range in 
top diameters even for these purposes, the top diameter limit, and 
consequently the waste, increasing in regions of poor markets. The 
top diameters used in constructing tables of merchantable volume 
must be clearly stated. For peeled wood, diameter inside bark is given. 

The minimum top diameter usually does not coincide with an 
exact merchantable length, but when a length of 4 feet is used, the 
practice may be adopted of accepting the last 4-foot stick which measures 
the minimum diameter at the middle of piece. The average top diameter 
will then coincide with the minimum established, half the sticks being 
slightly below this limit at the top end. 

The merchantable top diameter, combined with the minimum length 
of a merchantable piece, indicates the smallest size of tree measured 
at B.H. which can be shown in the volume table. Ordinarily, the mini- 
mum commercial diameter limit will be somewhat larger than this, 
based on the inclusion of cost of logging as a factor preventing the 
marketing of trees with the minimum merchantable contents. Volumes 
of trees of still smaller sizes can be shown only in tables for total cubic 
volume. Since the merchantable limit of top diameters for cordwood 
is small, in constructing standard volume tables for cubic feet or cords 
the trees are classed by D.B.H. and total height, in 5- or 10-foot height 
classes, as for tables giving total volume. 

148. Stump Heights. Stump height varies with local custom and 
with the scarcity and value of the wood. Stump heights, especially 
for large trees, are not uniform but increase with the diameter of the 
tree, and rules for cutting usually recognize this fact, specifying for 
instance that the height of stump shall not exceed one-half its diameter. 
For small timber, uniform stump heights may be specified, as low as 
from 1 foot to 6 inches. If the stump heights used in constructing the 
volume table are stated it enables the cruiser not only to know whether 
the table conforms to local usage, but to correct it for difference in 
practice. 

The cutting of low stumps not only increases the merchantable 
contents of the tree but will greatly increase the possibility of error 
by use of Smalian formula for volume. This error is always plus and 
will require special measurement of short lengths in butt log. 

149. Merchantable versus Used Length. Where the portion of the 
tree which is actually used falls short of the full possibility, due to care- 
less supervision or to failure to appreciate the economic conditions. 



WASTE, DEFINITION AND MEASUREMENT 179 

there arises a difference between the definition of merchantable length, 
and used length. Merchantable length is the total length of a stem 
which can be used under given conditions. Used length is the total 
length of a stem actually utilized in commercial operations. There 
is therefore no fixed or absolute merchantable length, since the very 
definition of the term " merchantable " indicates that the product 
must be salable. When an operator is actually utilizing all the material 
that he can manufacture or market at a profit used length and merchant- 
able length coincide. 

150. Waste, Definition and Measurement. Waste is therefore 
defined in two ways. First, there is the unavoidable waste in twigs, 
branches, stump and top, that cannot be used under existing economic 
conditions, logging costs, and markets. A better term for this material 
is refuse. This waste was large in earlier periods and tends constantly 
to diminish. Second, there is avoidable waste, caused by the fact 
that the markets and logging possibilities have changed faster than 
the logging practice. During the war this form of waste increased in 
certain sections due to the inefficiency, indifference and independence 
of woods labor. The amount of this avoidable waste is somewhat a 
matter of judgment. When waste is demonstrated, practice tends 
to take up the slack, and used lengths are readjusted to coincide with 
merchantable lengths. 

The unavoidable waste is usually taken as the difference between 
the total and merchantable volumes of the bole, excluding branches. 

For tops, the paraboloidal formula V = ^l is used, while for stumps, 

the cylindrical contents of the stump based on its upper area is usually 
accepted in place of its actual total volume. 

The avoidable waste represents the cubic volume of the top section 
between the upper limit of used length and the merchantable diameter 
limit, plus the cylinder representing the difference between actual 
height of stump and height to which it should have been cut. 

A more complicated method applied to board-foot contents is to 
re-scale the contents of the tree, measuring the top diameter of each 
log at a point lower than the existing point by the difference in stump 
height. The difference in total tree scale so obtained is regarded as 
indicating the waste. 

151. Defects or Cull. For pulpwood, defective or rotten pieces are 
not merchantable. This raises the question of cull or deductions from 
the cubic volume table. The question is far more sei'ious for board- 
foot volume tables. No such deductions should be made for cull in 
the volume tables themselves, especially in standard tables. The cull 
per cent varies without any reference to tree form or total volume. 



180 STANDARD VOLUME TABLES 

The deduction of a given per cent for cull would ruin the table, making 
of it a local table applicable only to timber which is assumed (one can 
never know certainly) to show the given per cent of defect. Even if 
the per cent of deduction is stated, the table would require complete 
recalculation for stands varying from this per cent of cull. By contrast, 
tables made for sound trees permit of the calculation of total volume 
for trees or stand, after which the estimated per cent of cull may be 
deducted from this total. 

All volume tables should be constructed to show only the volume 
of trees as if sound. They are based on exterior measurements or 
form, without deduction for interior defects, which must always be made 
by the cruiser from observation of the character of each separate tree 
or stand. 

152. Conversion of Volume Tables for Cubic Feet, to Cords. As 
seen in Chapter IX the ratio of cubic to stacked volume increases with 
the diameter, straight ness and smoothness of the average stick and vice 
versa. Tables of cubic volume may be converted into cords by the 
use of ratios or converting factors, but if a constant ratio is used for 
trees of all sizes, the corded or stacked contents of small trees will over- 
run, the values shown, while that of the larger trees will fall below it. 
Fixed ratios, of which 90 cubic feet per cord, or 70 per cent is an example, 
have the merit of standardizing the cubic or solid contents per stacked 
foot for trees of all sizes, regardless of their actual stacked volume. 
By mixing the cordwood from large and small trees, the average ratio 
might be attained in practice. The best example of this principle is 
the Humphrey caliper rule, which converts cubic to stacked measure 
by the ratio of 100.5 cubic feet per cord or 78.5 per cent. If this principle 
is adopted, the volume for each tree class is divided by the number of 
cubic feet per cord, which converts the table to the form desired. 

Where actual stacked volume is desired for trees of each size, the 
ratio of conversion nmst be found separately for the different size 
classes. The tree, and not the bolt of cordwood, is the unit to be meas- 
ured, hence the average size of the cordwood from trees of different 
sizes determines the converting factor. But few tables have been pre- 
pared on this basis. The most satisfactory method is to stack the cord- 
wood from trees of different diameters separately and determine the 
factors directly. A simpler method is to determine the diameter of the 
average stick in the tree, and apply the ratio previously found to hold 
good for cordwood of this average size. 

The ratio or ratios used for conversion should always be shown 
in connection with cordwood volume tables. 

An example of the converting factors used in constructing cord wood volume 
tables for second-growth hardwoods is given in Table XXXII. 



DEFECTS OR CULL 



181 



TABLE XXXII 

Conversion Factors for Second-growth Hardwoods by D.B.H. Classes with 
Corresponding Diameters of the Average 4-foot Stick in the Tree or 
IN THE Stack * 





Chestnut 


Black Oaks 


White Oaks 


Tree 














diameter 














breast-high. 


Diameter 


Conversion 


Diameter 


Conversion 


Diameter 


Conversion 




average 


factor 


average 


factor 


average 


factor 




stick. 


per cord. 


stick. 


per cord. 


stick. 


per cord. 


Inches 


Inches 


Cubic feet 


Inches 


Cubic feet 


Inches 


Cubic feet 


1 


0.9 












2 


1.8 


63 


l.S 


63 


1.8 


63 


3 


2.6 


70 


2.5 


69 


2.5 


69 


4 


3.3 


75 


3.1 


74 


3.1 


• 74 


5 


4.0 


79 


3.6 


77 


3.5 


76 


6 


4.7 


83 


4.1 


80 


3.9 


79 


7- 


5.2 


85 


4.5 


82 


4.2 


81 


8 


5.8 


88 


4.8 


84 


4.5 


82 


9 


6.2 


89 


5.0 


85 


4.7 


83 


10 


6.7 


91 


5.3 


86 


4.9 


84 


11 


7.0 


92 


5.4 


86 


5.0 


85 


12 


7.4 


93 


5.6 


87 


5 1 


85 


13 


7.7 


94 


5.7 


88 


5.2 


85 


14 


7.9 


94 


5.7 


88 


5.2 


85 


15 


8.2 


95 


5.8 


88 


5.3 


86 


16 


8.4 


95 


5.9 


88 


5.4 


86 


17 


8.5 


95 


5.9 


88 






18 


8.7 


95 


6.0 


89 






19 


8.9 


96 


6.0 


89 






20 


9.0 


96 











* Second-Growth Hardwoods in Connecticut, E. H. Frothingham, U. S. Forest Service, Bui. 96, 
1912, p. 64. 



From a table showing the contents in cords, by either of the above 
standards, for trees of each size class, a second table can be constructed, 
giving the number of trees of each class requn-ed to produce one cord 
of wood. The cubic contents of a cord, according to the ratio adopted, 
is divided by that of the tree as shown in a volume table. This gives 
the number of trees required. These tables may be of value in estimat- 
ing cordwood, by making rough counts. The principle involved is 
the same as that used in estimating board feet by log run (§ 120). 



CHAPTER XIII 
VOLUME TABLES FOR BOARD FEET 

153. The Standard or Basis for Board-Foot Volume Tables. In 

Chapter X it was shown that the basis of measurement for standing 
timber intended for sale is either the possible sawed output for tracts 
that are cut by local mills, or the log scale for timber to be transported 
to mills at some distance from the area. Even in the first instance 
the measurement of tree volumes requnes a local log rule based on 
mill tallies. 

Volume tables for board feet must be based upon the contents of 
the logs which can be cut from sound trees, as measured by the stand- 
ard or log rule which forms the basis of sale of the timber. For the 
purpose' of timber estimating for which these tables are required, it 
is not permissible to substitute volumes representing a different stand- 
ard even if a more accurate one. 

But it is recognized that existing conditions requiring the scaling 
of logs by defective log rules may change and for purposes of stock 
taking or inventory of standing timber required by an owner for the 
management of forest property which he intends to retain, and for the 
prediction of growth, volumes of standing timber are preferably meas- 
ured by tables based on log rules which give an accurate measurement 
of the board-foot contents of the trees. 

This conflict between a temporary economic condition and a per- 
manent basis of management may require a double standard of measure- 
ment, and two separate volume tables. The first step in the con- 
struction of volume tables for board feet is to decide upon the log rule 
to be used in obtaining the tree volumes. 

For second-growth timber, and for the purpose of inventory and 
basis of growth studies, this should if possible be a rule such as the 
International, or one based on mill tallies of lumber such as the Massa- 
chusetts log rule. 

For commercial timber estimating it must of necessity at present 
be the log rule in common use in the locality. 

154. Adoption of a Standard Log Length. The standard practice, 
in measuring the contents of entire trees for the construction of board- 
foot volume tables is to disregard the actual log lengths as sawed, and 
to measure the diameter on the bole at fixed points corresponding to 

182 



TOP DIAMETERS, FIXED OR VARIABLE LIMITS 183 

logs of a standard length, since this basis coincides with the application 
of the table by timber cruisers (§ 119). Sixteen feet is the standard 
most commonly adopted, to which is added a trimming allowance of 
.3 foot. Volume tables for hardwoods may, if advisable, be based on 
logs 12 feet long but this is the exception. The objections to the alter- 
native method of scaling the contents of the logs as sawed are summed 
up in § 135, but this latter method has been extensivel}'^ used in the past 
in volume-table construction. The base from which log lengths are 
measured is usually the actual height of the stump, as sawed. This 
introduces a variable factor dependent upon the standard of heights 
secured in felling. 

155. Top Diameters, Fixed or Variable Limits. The field measure- 
ments of tree volumes are the same as for cubic contents of logs (§ 135). 
If 16 feet is the standard log length, the taper measurements are com- 
monly recorded for each 8-foot point as well. The purpose of the work 
is to determine the merchantable contents. This evidently calls for 
the omission of the volume of the top portion of the bole, which is not 
merchantable. But shall the length of the rejected top be based upon 
the actual utilization of the specific tree? If so, the last saw cut will 
indicate the limit of merchantability, beyond which the contents of 
the top is classed as waste. By the method of measuring the volume 
of the logs as sawed, this top is rejected as it lies, regardless of whether 
the utilization of the tree has been close or wasteful. If on the other 
hand diameters are taken at fixed intervals, the point of measurement 
will seldom coincide with that of the last cut, but will fall above or 
below it. 

If actual utilization practice is to be adopted as the basis of the 
table, while at the same time the fixed length of section is to be retained, 
the top diameter of the last " merchantable " log for the volume table 
should be taken at the point which falls the nearest to the last saw cut, 
whether this point is above or below the cut. When the saw cut is 
midway between two points, the lower measurement may be taken, 
or else the character of the bole may be made the basis of choice (p. 184, 
Fig. 30). 

When, by method B, only the merchantable volume is desired, if last cut is 
at (1), the volume will be taken to the nearest 8-foot point Be. If cut at (2), Be 
is still the nearest point. But if cut at (3) equidistant from Be and B7, either the 
upper point B7 would be chosen on alternate trees or the point best representing 
merchantable volume, in this case Be. 

Utilization, especially where sawlogs are cut from trees with limby 
tops, is seldom to a uniform diameter. The actual top diameter varies 
widely but the average increases with the D.B.H. of the tree. By the 
method outlined above, the contents of the volume table are made to 



184 



VOLUME TABLES FOR BOARD FEET 



•H'aa-^ 



au 



m— > 



-5 W 



_§ o ^ 

' S o -- 

o c, S 






m-:^ 



coincide with the portion of the tree which is actually used, and the 
average top diameter with that which is actually cut. 

But the variable practice of sawing and the arbitrary standards 
set by saw crews as to waste in the tops, differing with different crews, 

logging jobs, regions and seasons, is a strong 
argument for adopting a fixed standard for 
top diameters for saw timber. This stand- 
ard may either conform to the average 
diameter utilized, or may depart from it 
and be smaller; e.g., as at By. 

Where a fixed top diameter is chosen, 
instead of the variable one coinciding with 
utilization practice, the last taper measure- 
ment will usually fall above or below this 
diameter, as before. Here the same rule 
of give and take can be applied; but if the 
diameter limit is small the top tapers rap- 
idly and it may be preferable to take no 
measurement of less than the minimum top 
diameter. The last top measurements will 
then fall always either at or below the 
point. 

Where 16-foot measurements only are 
made, it is necessary to take an 8-foot 
length at the top whenever the last cut 
falls more than 4 feet distant from the last 
16-foot taper. This is another reason for 
taking 8-foot tapers throughout. 

156. Defective Trees, Measurement. 
Frequently one or two top logs in certain 
trees will not be utilized because of defects 
in the upper portion of the bole. Where 
the table is based on actual utilization, 
such trees should be rejected for measure- 
ment or else the defective logs should be 
measured, since the cull is not due to form 
but to defect. Where the top diameter is 
fixed independent of the last cut, these defective trees should be 
measured. All trees are suitable for volume measurements except 
forked-topped trees, those with abnormal D.B.H. dimensions due 
to butt swelling and frequently caused by fire scars, and trees 
deformed in such a manner that a series of normal taper measure- 
ments cannot be obtained. Abnormalities at a given taper point 



ii- 

5 ^ S ^ 

=? O fcH C 

t- " " c3 
<B 03 C 3 

-"^ .^ •— '^ 
M o '^ cc 

B 3 ^ "^ 

IS ^ O bC 
c3 S ^ -2 



o 



« g " 0. 






^3 ci 






<^--^ 



BASIS FOR TREE CLASSES 185 

can be overcome by proper methods of measurement (§ 25). It 
is the purpose of volume tables to show average volumes for sound 
trees. Since defective logs or trees will be scaled as if sound in volume 
table construction, they are suitable for this purpose. 

157. Total versus Merchantable Heights as a Basis for Tree Classes. 
Where cubic contents, either total or merchantable, are the basis of 
tree volumes, the total height of the tree to tip of crown is the only 
serviceable basis of classification by height (§137). Where the volume 
of the tree is desired in merchantable units of product, such as board 
feet, the height desired in practice is the merchantable length of the 
bole or height of the top of the last log. Timber cruisers commonly 
use the number of logs of given length in a tree, and not the total height 
in feet, to obtain the contents. The practice of basing height on the 
merchantable length of bole is most useful where the proportion of total 
length used is most variable, as in large hardwoods or heavy-limbed 
conifers, and where there is an evident variation between actual top 
diameters utilized. Total heights in dense stands of tall old trees are 
hard to see and measure while the top diameter limit is usually visible. 
This basis is used almost universally in the estimation of old-growth 
timber of all species. 

The same height basis must be used in timber estimating as is used 
in the tables, if volume tables are to be employed. Hence the method 
of measuring heights in cruising will be either determined by the existing 
tables, or else the tables must be constructed on the basis desired for 
the estimating. The measurement of trees for the construction of vol- 
ume tables should therefore include both the total and merchantable 
height, to permit of constructing tables on each basis for use as desired. 

158. The Coordination of Merchantable Heights with Top Diam- 
eters. The use of volume tables to determine contents of standing 
trees requires the determination in the field of but two dimensions, 
namely D.B.H. and height, and is based on the assumption that the 
volume of an average tree of these dimensions gives the average volume 
of the trees of the same sizes in the stand to be estimated. Where 
total height is used as the basis, there is little opportunity for error in 
applying the volumes in the table, since but one point on the tree can 
be measured for height, namely the tip. But where merchantable 
height is the basis, a second variable is introduced, the top diameter. 
The volume now depends, not on one definite factor of height as before, 
but on securing coordination between these two variables, i.e., height 
of merchantable top, and diameter of merchantable top, in the applica- 
tion of the volume table. 

The choice of top diameter limits has been discussed. But the 
effect of this choice upon the merchantable length (the height), in 



186 



VOLUME TABLES FOR BOARD FEET 



such tables, needs special emphasis. If a large top diameter is adopted, 
the merchantable height is correspondingly less for trees of the same 
total height and form. A tree 100 feet high may have five logs, 16 
feet long, if cut to 10 inches, but if cut to 16 inches instead, it may be 
only a four-log tree. A 6-inch top may in turn 
give 88 feet or 5| logs from the same tree. Thus 
top diameter increases as merchantable length 
diminishes. Whatever coordination between 
these two variables is adopted in constructing 
the volume table will have to be used in applying 
it; i.e., the same top diameters used for the 
table must be used as the basis of merchant- 
able heights in timber estimating. Failure to 
observe this rule may result in serious errors 
and has sometimes brought the use of such 
volume tables into disfavor among practical 
cruisers. 

The results of such lack of coordination are easily 
illustrated, bj' comparing the volumes of trees, when 
divided into 16-foot cylinders and scaled as logs. 
Since the frustum of a cone is a regular solid resembling 
the merchantable portion of the bole, it serves to illus- 
trate the principle in question. Assume that a 6-inch 
top has been adopted as a standard, and all trees meas- 
ured to that point. 

A four-log tree, 15 inches at the top of the first log, 
inside bark, is assumed to have 3 inches taper per log. 
The volume of this tree, by the International log rule, 
will then be 




Fig. 31.— Cause of 
errors in use of vol- 
ume tables, when 
based on merchant- 

, able heights and 
fixed top diameters. 



Logs 


First 


Second 


Third 


Fourth 


Total for 
four logs 


Diameter, inches 

Volume, board feet .... 


15 
175 


12 
105 


9 
55 


6 
20 


355 



In estimating, if this table is to be used, the only 15-inch four-log tree whose 
volume can be correctly measured is one which tapers 3 inches per log, and hence 
has a 6- inch top diameter. But the cruiser may fail to observe the same coordi- 
nation between merchantable length and top diameter, and may tally a 15-inch tree 
which tapers 2 inches per log, as a four-log tree. The dimensions of this tree up to 
the top of the fourth log are 



Logs 


First 


Second 


Third 


Fourth 


Total for 
four logs 


Diameter, inches 

Volume, board feet .... 


15 
175 


13 

130 


11 

90 


9 
55 


450 



MERCHANTABLE HEIGHTS WITH TOP DIAMETERS 



187 



This tree, if measured to 6 inches, has the additional length of I5 logs, whose 
volume is 



Logs 


Fifth 


Half of 
sixth 


Total 
additional 


Total for 
55 logs 


Diameter, inches 

Volume, board feet 


7 
30 


6 
10 


40 


490 



The recording of this tree as a four-log tree was probably based on the fact 
that it would actually be cut at 9 inches in the top instead of at 6 inches. But 
the cruiser, if he uses this volume table, does not obtain from it the volume of a 
tree with a 9-inch top, but of one with a 6-inch top. The initial error for this tree 
consists in not tallying it as a 5§-log tree with a 6-inch top. If the full contents 
of the four actual logs which it contains could be obtained from the table, the 
error would be the loss of 40 feet in the I5 logs not measured. This is 8 per cent 
of the total tree volume. But instead, a much greater additional error is incurred. 
The volume given in the table is for a four-log tree with a 6-inch top containing 
355 board feet instead of one measuring 9 inches at top. This error, due to differ- 
ence in top diameter not only of the last log but of the remaining logs, is 95 board 
feet (450-355) or 21 per cent.' 

If the purpose of the estimate is to obtain, not the volume of all trees to 6 inches, 
but the volume actually to be cut, the attempt to obtain this by dropping the 
merchantable length of this tree to the 9-inch point, Ig logs below the 6-inch point, 
has made the use of the above volume table impossible, for in place of a correct 
deduction of 8 per cent from the true volume of a 5^-log tree, which would give 
the true volume merchantable, the use of the table has lowered the estimate by 
27 per cent, which is |-|^ of the desired estimate or 21 per cent too low. Errors 
of this magnitude and even greater may and have been made in use of volume tables, 
solely from this source. 

The coordination evidently demands: 

The estimation of height to the same point which has been used 

in constructing such a table. 
The deduction of the requisite per cent, representing the small 
top log or logs, to obtain net merchantable volume, in case 
utilization falls short of this point. 
Errors in estimating merchantable heights, if consistently too great 
or too small, incur both the above errors when the tally is applied to 
the volume table. Other methods of avoiding these errors are: 
To use total height as a basis. 
To measure a few heights carefully instead of guessing at many 

or all heights. 
To construct the table so as to coincide with used top diameters, 
and then exercise care in employing this same standard in 
estimating.! 

^ The writer's initial experience in timber cruising was with W. R. Dedon, in 
Minnesota. Mr. Dedon did not believe in the use of volume tables, claiming that 



188 VOLUME TABLES FOR BOARD FEET 

159. Construction of Board-foot Volume Tables. The basis agreed 
upon as to the top diameter to use, if merchantable heights are utilized, 
will determine the height class into which each tree falls. The steps 
in construction are the same as for tables of total cubic volume (§ 131) 
with the following exceptions. 

Compute the volume of each tree by means of the log rule chosen, 
by scaling each 16-foot log. In volume table work, this scale per log 
should preferably be interpolated to yV-inch values, for which purpose 
the values of the log rule can be tabulated for the given interpolations. 
The last or top log if 8 feet long is scaled as one-half the volume of a 
16-foot log of equal diameter. If the logs are not scaled to yV-inch 
they are rounded off to nearest inch above or below (§ 137) but where 
but a few trees are measured in each size class, this incurs the risk of 
unnecessary variations in volume of the tree classes. 

When merchantable heights are taken to fixed lengths, the variable 
at this point will be the top diameter. Therefore, the average top 
diameters should be showm for each diameter and height class. These 
tops may later be averaged solely on the basis of diameter at breast 
height. 

160. Data Which Should Accompany a Volume Table. Because 
of the errors possible in misapplying tables for merchantable volumes, 
as set forth, the use of such volume tables presupposes knowledge of 
their reliability and applicability. For this purpose the following data 
should always accompany the tables: 

Species. 

Region or locality where measurements w^ere taken. 

Age of trees to which values apply, when distinguished. 

Sites or quality to which values apply, when distinguished. 

Unit of volume used. 

Log rule if in board feet, or mill tallies specifying character and 

thickness of lumber included. 
Specifications, if for piece products. 
Number of trees measured as basis, by diameter classes. 
Height of stumps. 

on the only occasion on which he had attempted it, the table gave just half of the 
true estimate. This was unquestionably due to the cause explained above, that is, 
trying to coordinate large top diameters with a table made to smaller tops. The 
first impression, in using a table constructed to a small top diameter is that it 
"secures a greater volume per tree." The error is just the reverse of this — it 
under-estimates the timber. If, on the other hand, the top diameters in the table 
are larger than those applied in the field and the per cent of total contents less, 
the error in applying the table is an over-estimate equally great. These possi- 
bilities of error in the use of volume tables based on merchantable length have 
been commonly overlooked in practice. 



CHECKING THE ACCURACY OF VOLUME TABLES 189 

Top diameters used — by diametei* classes if variable. 
Method used in constructing table, 

a. Based on measurements at fixed intervals. 

b. Based on measurements of logs as cut. 

c. From tables of taper or form (Chapter XV). 

d. From form factors (Chapter XVI) 
Author, and year of preparation. 

The basis of classification of volumes, as to height and diameter, 
is shown in the table itself. But tables based solely on diameter will 
have their value increased if the average heights used in constructing 
the table are also shown (§ 162). 

161. Checking the Accuracy of Volume Tables. Volume tables 
make no pretense of giving accurately the volume of single trees (§ 121). 
If the average values given coincide with the average of the volumes 
of the trees to be measured, the table is accurate for the purpose in hand. 

But, although applied correctly (§158) volume tables will gi\c 
inaccurate results, first, if the table itself is inaccurately made and does 
not give correctly the volumes of the trees from which it was constructed, 
second, if the trees to be measured average greater or smaller volumes 
for given diameters and heights than those given in the table, on account 
of fuller form or vice versa. 

Volume tables made in one locality may be serviceable in other 
regions, covering the entire range of a species. If the estimates are 
made to conform with the top diameters and log rules used in the table 
the only possible variation in volume from such tables is that of average 
form, and variations due to this factor can be determined without 
constructing an entirely new table (§ 171). 

To check the accuracy of construction of a table, the basis in trees 
is first considered. Tables based on from 500 to 1000 trees or more 
are regarded as fairly reliable, while if fewer trees have been used the 
table is open to question. The total actual volume of the trees used 
in constructing the table can be checked against the total volume of 
the same trees figured from the table. This gives a basic check which 
may, however, conceal compensating errors. The average volume of 
the trees in each diameter and height group may then be checked 
against the tabular values in the same way, and the errors recorded 
in terms of per cent. These errors should compensate. A still more 
accurate check is to record the divergence in volume of each tree from 
the tabular volume and total the per cents of error plus and minus, 
which should compensate. Or, the plus and minus errors may be 
plotted to detect any trend towards high or low values at one end or 
the other of the curves. 



190 VOLUME TABLES FOR BOARD FEET 

To test the accuracy of a table of proved value, when applied to 
a specific stand or region, the volume of as many trees as convenient, 
preferably about 100 trees, is determined by the same standards as used 
in the table. The per cent of divergence of the actual volumes, one 
by one, from those of the table, is computed. These per cents 
may be tabulated and averaged by diameter and by height; if they 
reveal a consistent difference in volume, the values of the table can be 
raised or lowered by the average per cent indicated. 

References 

The Problem of Making Volume Tables for Use on National Forests, T. T. Munger, 

Journal of Forestry, XV, 1917, p. 574. 
The Height and Diameter Basis for Volume Tables, Donald Bruce, Journal of 

Forestry, Vol. XVIII, 1920, p. 549. 
A Proposed Standardization of the Checking of Volume Tables, Donald Bruce, 

Journal of Forestry, Vol. XVIII, 1920, p. 544. 
Top Diameter in Construction and Application of Volume Tables Based on Log 

Lengths, H. H. Chapman, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 221. 



CHAPTER XIV 

VOLUME TABLES FOR PIECE PRODUCTS, COMBINATION 
AND GRADED VOLUME TABLES 

162. Volume Tables for Piece Products. The purpose of volume 
tables for piece products is identical with that for board feet — to enable 
the timber estimator to dispense with the necessity of judging by eye 
the contents of separate trees, and substituting therefor merely the 
record of diameters and heights. 

Volume tables for piece products are limited in scope. The speci- 
fications as to size of the product are the governing factor. For poles, 
no volume table is needed. For small products such as staves, it is 
almost impossible to make volume tables, on account of the effect of 
cull in reducing the output and the difficulty of judging this in the 
standing timber. Even here, tables showing the number of staves 
of given dimensions in perfect trees of different diameters, or in sections 
or bolts of different diameters may be of help in estimating. Here, 
as elsewhere, the cull factor cannot be introduced into volume tables 
but must be applied as a reduction factor to their contents. 

To construct a volume table for any specific product, the same 
methods used in constructing log rules can be applied ; first, the number 
of pieces of certain dimensions which can be cut from logs or bolts of 
given diameters can be found by plotting with cross-section of the 
standard piece upon the areas of circles. Second, these theoretical 
results can be checked against the actual number of pieces hewn or 
sawed from logs or bolts of the same diameter. The second check 
is to ascertain the effect of irregular shapes, and of methods of cutting 
or manufacture, as affected by the grain of the wood and tools used. 
In such a check, only sound logs are taken, but the factor of cull may 
be studied at the same time. The contents of these logs can then be 
combined into volume tables by the methods outlined in Chapter XL 

163. Volume Tables for Railroad Cross Ties. The most useful 
volume tables for such products are those for railroad cross ties. Just 
as for poles, the length of the ties, usually standardized at 8 feet, is 
a partial indication of the number of ties which can be cut from trees 
of given sizes. Hewn or pole ties, flattened on the faces only, are cut 
only from trees or the upper portion of boles which are too small to 
produce two or more ties from one bolt. Volume tables are needed : 

191 



192 VOLUME TABLES FOR PIECE PRODUCTS 

1. For trees of larger diameter, to show the number of ties which 
can be obtained from each bolt, hence from the tree. 

2. To show the number of ties of different grades as determined 
by size, which can ])e obtained from each bolt, and from the tree. 

This latter requisite also applies to bolts from which but one tie 
can be cut. 

A good example of a tie-volume table is that prepared ' for western larch and 
Douglas fir, Kootenai National Forest, Idaho, in 1919, for the five standard grades 
of hewn railroad ties specified by the U. S. R. II. Administration. The dimensions 
called for are: 

No. 1. 6 inches by 6 inches by 8 feet. 

No. 2. 6 inches by 7 inches by 8 feet. 

No. 3. 7 inches by 7 inches by 8 feet. 

No. 4. 7 inches by 8 inches by 8 feet. 

No. 5. 7 inches by 9 inches by S feet. 

Each tree was measured at 8-foot intervals for diameter inside bark. The 
method was to construct a taper table (§ 167) from which the sizes of pole ties 
which could be cut from each bolt were determined. The steps were: 

1. Determine the average top diameter inside bark required to produce a tie 
for each standard size. These were: 

For No. 1. 8.5 inches. 

No. 2. 9.2 inches. 

No. 3. 9.9 inches. 

No. 4. 10.6 inches. 

No. 5. 11.4 inches. 

2. Separate the trees measured into D.B.H. and height classes. The height 
classes used were the number of 8-foot lengths in the merchantable bole, to a top 
diameter of 8.5 inches. 

3. Determine the average diameter at each 8-foot point, for the trees in each 
of these separate groups. This gives a series of taper measurements and an average 
form for the tree. 

4. With distance above stump as the independent variable, on the horizontal 
scale, and top diameter of each tie (each 8-foo4; point) as the dependent variable 
on vertical scale, plot the average diameter at each 8-foot point. By connecting 
these points the form of the tree is shown. These curves are used to smooth out 
irregularities in values. 

5. From the average upper diameter of each 8-foot bolt, for trees of each D.B.H. 
class, and separate height classes, as 5-tie trees, 6-tie trees, etc., the class of tie 
which can be cut from each bolt is indicated, and the number of ties of each grade 
in the tree is shown. This constitutes the tie-volume table. Instead of recording 
merely the total number of ties, regardless of grade, which could be done without 
the table, the estimator now has his products classified. 

The same method can be used for trees whose dimensions permit of sawing or 
splitting two or more ties from one bolt, but usually trees of this diameter will 
be measured in part as sawlogs in board feet rather than as sawed or split ties. 

^ James W. Girard and W. S. Schwartz. 



COMBINATION VOLUME TABLES 193 

164. Combination Volume Tables for Two or More Products. 

Close utilization of tree volumes requires the measurement of two or 
more classes of products, such as saw timber and residual cordwood, 
saw timber and residual mine props, railroad ties and residual mine 
props. 

In all tables of this class, the method of construction is to determine 
the diameter which limits the sizes used for the higher purpose, and then 
to measure the contents of the remainder of the bole to the smaller 
diameter which limits the sizes used for the residual product. The 
measurements must be taken on the felled tree before any portion is 
skidded off. 

For example, in constructing a sawlog, tie, prop table for lodgepole 
pine, on the Arapahoe National Forest, Colorado, 6 inches was used 
as the top diameter for sawlogs, to be scaled by Scribner Decimal C 
log rule. Five inches was the top diameter for mine props. The 
number of feet remaining in the top, between 6 and 5 inches, was 
recorded as linear feet. In the same manner, 10 inches was fixed as 
the top diameter for the production of hewn ties (this has now been 
lowered to 8.5 inches by new specifications), and the number of ties 
in each tree, to this point, recorded. Above 10 inches, the 8-foot 
lengths are entered as prop material.^ 

The residual cordwood in the tops of trees cut for sawlogs or ties 
is measured as for cubic feet. Where the volumes for the more valu- 
able product are measured to a fixed top diameter, the problem of resid- 
ual volume is easily solved. Where top diameter varies with other 
factors, the amount of cordwood in the tops varies accordingly. This 
variation is further increased when branch-wood or lapwood is included. 
Tables usually express the volume of residual . cordwood in terms of 
decimal fractions of cords per tree, and the data are frequently simplified 
by averaging the contents on basis of diameter. 

165. Graded Volume Tables. A graded volume table is an attempt 
to show the amount of different standard grades of lumber which may 
be sawed from trees of different dimensions. Its purpose is to aid in 
estimating the value of standing timber. The preparation of graded 
volume tables is one of the objects of mill-scale studies (§ 74). The 
basis of these tables is the sawed lumber produced from logs. To 
coordinate these data with the volume of standing trees, the following 
points must be considered: 

1. The logs sawed are usually cut into variable log lengths and 
cannot be standardized to a given length, such as 16 feet. 

2. In sawing logs, especially hardwoods, the resultant output will 

1 Ref . Volume Table for Lodgepole Pine, A. T. Upson, Forestry Quarterly, 
Vol. XII, 1914, p. 319. 



194 VOLUME TABLES FOR PIECE PRODUCTS 

be determined by the amount of defect in the log as well as the grades 
of lumber — the net, not the gross scale will be obtained. 

But the same objections hold against introducing into graded tables 
the variable factor of the cull due to a great range of defects as have 
operated to exclude such deductions from all standard tables. Hence 
the only safe standard on which to construct such tables is sound logs. 

3. The grades of lumber are first determined in logs of given diam- 
eters and lengths, from which graded log rules may be constructed. 
Such rules are of course never used in scaling logs (§ 87) but solely to 
aid in the determination of the average price to be paid for the contents 
as scaled. 

4. The grades of lumber in trees of different sizes must be obtained 
by correlating the sizes of the logs graded with the logs contained in 
the trees. 

One standard method used in constructing such tables is to follow 
the logs from different trees through the mill, by numbering the logs 
in the woods, a process impossible without much delay except in small 
jobs. 

Separation of butt logs and top logs is a less detailed method of 
classification of logs. 

A third plan is to prepare separately the graded log table without 
reference to the trees, and then determine the sizes of logs in trees of 
different D.B.H. applying the grades to the given logs to get the grades 
for the tree. Of the three methods, this is the most practical and use- 
ful. In this the graded log table is the real basis, local graded volume 
tables being constructed from this table for use in each different stand 
of timber (§87). 

5. To show the actual contents of trees of each separate diameter 
and height class, expressed in from four to eight standard grades would 
call for a table of considerable bulk, and when in addition to this draw- 
back the actual volumes shown are based on an arbitrary net sawed 
output minus whatever cull happens to have been present in the logs 
measured, the advisability of using such a form of standard table is 
questionable. 

6. Where graded volume tables of greater permanent value are 
desired the purpose of the tables will be accomplished by the following 
simplification: 

a. Substitute per cents of sawed contents for actual sawed con- 
tents for each grade of lumber scaled. 
h. Substitute D.B.H. alone for D.B.H. and height, as the basis 
of classification of the trees. 
If these per cents apply to sound logs, they may require modifica- 
tion in the case of defective timber. Wliere heart rot is prevalent 



GRADED VOLUME TABLES 195 

it causes a greater loss in the middle portions of logs which on account 
of the presence of knots are of lower grade than the sound outer portion. 
On the other hand, cat face and exterior defects reduce the amount 
of clear lumber of upper grades. Unless such factors can be judged 
correctly, the same per cents of grades must be accepted for defective 
logs as are shown in the table for sound logs. 

It has been the common practice, in preparing graded volume 
tables for hardwoods, to base the table upon the net sound contents 
after deducting cull. Where sufficient typical sound logs of the larger 
sizes cannot be obtained, the drawbacks of a table based on a partial 
scale, i.e., culled, can be in a measure overcome by reducing this table 
to per cent form as indicated above. Such a table should include a 
statement of the basis on which it was made, the average per cent 
of cull deducted, and the general character of the defects and influence 
on the different grades. On this basis, its application to other timber 
is possible.^ 

Graded log tables are of permanent value, and the utility of these 
tables, if expressed in per cent, may be greater than is now imagined. 
The permanence of such a table depends entirely on the maintenance 
of the standard of grading, or gi'ades of lumber on which the graded 
table is based, hence such tables cannot have the permanent scientific 
value of tables giving volume in standard units for sound trees. 

References 

A Volume Table for Hewed Railroad Ties, James W. Girard and W. S. Schwartz, 

Journal of Forestry, Vol. XVII, 1919, p. 839. 
Graded Volume Tables for Vermont Hardwoods, Irving W. Bailey and Philip G. 

Heald, Forestry Quarterly, Vol. XII, 1914, p. 5. 
The Ashes, Their Characteristics and Management, W. D. Sterrett, Bui. 299, 

U. S. Dept. Agr., 1915, p. 35. (Table based on per cents.) 
Grades and Amounts of Lumber Sawed from Yellow Poplar, Yellow Birch, Sugar 

Maple, and Beech, E. A. Braniff, Bui. 73, Forest Service, 1906. (Table by 

per cents for Yellow Poplar.) 
Assortment Tables, Mitteilungen der Schwarzerischen Centralanstalt fiir das forst- 

liche Versuchswesen, Vol. XI, 2 Heft, pp. 153-272. Review in Forestry 

Quarterly, Vol. XIV, p. 752. 
Graded Log Tables for Loblolly Pine, W. W. Ashe, Bui. 24, North Carolina Geolog- 
ical Survey, 1915. 

^ European investigations have shown that the per cent of total volumes which 
is obtained in the different grades of product varies with the diameter but does 
not differ appreciably with height. "In proportion as the shorter stem is less 
in volume than the longer, the assortment contents decreases but the per cent 
relation remains the same." Ref. Forestry Quarterly, Vol. XIV, 1916, p. 752. 



CHAPTER XV 

THE FORM OF TREES AND TAPER TABLES 

166. Form as a Third Factor Affecting Volume. While standard 
volume tables (Chapter XIj differentiate the volumes of trees of dif- 
ferent D.B.H. and heights, they make no distinction between trees 
having paraboloidal forms and those approaching the cone or neiloid 
(§ 26) in form, but seek to average the differences in volume caused by 
these variations. Occasionally two separate tables are made for a 
species, one for old trees, the other for young second-growth, since 
it has been found that the average volume of trees of these two age 
classes differed considerably. Any such difference, whatever its cause, 
is due to difference in form as indicated above, for trees which have the 
same D.B.H. and height. 

Volume tables have come to stay, since they substitute accurate measurements 
of D.B.H. and of height, which may be checked by calipers or hypsometers (§ 193), 
for too exclusive a use of the eye, and for the very uncertain method of guessing 
at or figuring out the volume of an average tree whose dimensions are in turn 
arrived at by guess or judgment. 

The difficidty of having to depend solely on volume tables of this character lies 
not in the tables themselves but, 

(1) in their incorrect application (§ 124); 
. (2) in their not being based on the same factors of volume determination as are 
desired for the estimate; 

(3) in the possibihty of not having any tables and being forced to construct them. 
To summarize here the factors in which the tables must agree with the basis of 
estimating we find: (a) Choice of unit of measurement as board feet, specific log 
rules, cross-ties, cords. (6) Closeness of utilization in tops and stump, (c) Point 
of diameter and height measurement, (d) Thickness of bark. (e) Variations 
caused by form independent of diameter and height. 

For these reasons the demand for some form of imiversal volume table in esti- 
mating is very strong. 

The substitution of a fixed taper per log, and the use of tables showing volumes 
for trees of the same diameter and height but with different rates of taper (§ 122) 
is an attempt to differentiate between trees with different form, but, in effect, 
this plan assumes that all trees have the same form, that of the frustum of a cone 
and differ only in being tall or short, or tapering slowly or rapidly up to the top 
diameter. 

The only satisfactory basis of a universal volume table is one in 
which all three of the variables, namely diameter, height, and form 

196 



TAPER TABLES, DEFINITION AND PURPOSE 197 

classes are distinguished. In tables based upon diameter and height 
only, no record of form is shown. The volumes as given in the table 
do not indicate whether the tree is full-boled or conical. This draw- 
back is further aggravated by the use of board-foot log rules whose 
values are not interchangeable. 

167. Taper Tables, Definition and Purpose. There are two methods 
for recording differences in the form of trees, form tables or taper tables, 
and form classes or form factors. 

A table which does not show the volume of the tree, but shows 
the actual form by diameters at fixed points from base to tip, is com- 
monly termed a taper table. From such a table, the volume of the aver- 
age tree for each diameter and height class can be measured as readily 
in the office as from the felled tree. Tables of volume can thus be 
constructed from a taper table, using any desired unit of product, 
such as cubic feet, board feet or piece products. They therefore form 
the basis for any required future volume table. For this reason, if 
taper measurements are taken at regular intervals, preferably 8.15 feet, 
from stump to top of tree, they constitute a permanent scientific record 
of tree form which will make it unnecessary to measure felled trees 
again for new volume tables. 

168. Methods of Constructing Taper Tables. Taper tables are 
based on total height- and hence they should record the form of the 
entire bole. 

A separate table is required for each height class showing the taper 
of trees of each diameter in this class; e.g., for white ash ^ tapers are 
shown for trees of 10-foot height classes from 30 to 120 feet. 

For each height class, and D.B.H. class, the diameter of the tree 
inside bark must be given at each fixed point, 8.15 feet or multiples 
thereof above the stump. 

The bole, below D.B.H. , tapers much less regularly than above 
that point, but a complete taper table should give the average diam- 
eter inside bark preferably at 1, 2, 3 and 4 feet from the ground. 

In Table XXXIII, p. 198, stump tapers are given, the diameter inside bark 
at B.H. and the upper diameters at 8.15-foot intervals from stumps taken as 
uniformly 1 foot high. But one class is shown, namely, 90-foot trees. A similar 
table is constructed for trees of each separate height class, such as 80-foot or 70-foot 
trees. 

When the taper measurements have been taken at fixed points 
on all trees, the average diameters at these points may be obtained 
directly from the original data. The process is shown in Table XXXIV. 

» Bui. 299 U.S. Dept. Agr., The Ashes, W. D. Sterrett. 



198 



THE FORM OF TREES AND TAPER TABLES 



TABLE XXXIII 

Form or Taper for White Ash Trees op Different Diameters under 75 
Years of Age, Giving Diameters inside Baiik at Different Heights 
ABOVE the Ground 

90-foot Trees 





Height amove Ground — Feet 










Diam- 
















eter 
breast- 
high. 

Inches 


1 


2 


3 


4.5 


9.15 


1 
17.3 23.45 33.6 41.75 49.9 58.05 66.2 74.35 

1 1 


Basis 
Trees 


Diameter 


INSIDE Bark — Inches 








8 


9.2 


8.5 


7.9 


7.3 


6.8 


6.4 


6.0 


5.5 


4.9 


4.2 


3.3 


2.3 


1.4 




9 


10.4 


9.5 


8.9 


8.2 


7.6 


7.2 


6.8 


6.2 


5.5 


4.8 


3.8 


2.7 


1.7 




10 


11.7 


10.6 


9.9 


9.1 


8.5 


8.0 


7.5 


6.9 


6.2 


5.4 


4.3 


3.1 


1.9 


1 


11 


12.9 


11.7 


10.9 


10.1 


9.3 


8.7 


8.2 


7.5 


6.8 


6.0 


4.9 


3.5 


2.2 


1 


12 


14.1 


12.8 


11.9 


11.0 


10.2 


9.6 


9.1 


8.3 


7.6 


6.6 


5.4 


3.9 


2.5 


3 


13 


15.3 


14.0 


13.0 


11.9 


11.0 


10.3 


9.8 


9.0 


8.2 


7.3 


5.9 


4.3 


2.8 


6 


14 


16.5 


15.1 


14.0 


12.8 


12.0 


11.2 


10.5 


9.8 


9.0 


7.9 


6.5 


4.9 


3.2 


7 


15 


17.6 


16.2 


15.0 


13.8 


12.7 


11.9 


11.2 


10.4 


9.6 


8.5 


7.0 


5.3 


3.5 


4 


16 


18.8 


17.3 


16.1 


14.7 


13.6 


12.7 


11.9 


11.1 


10.3 


9.2 


7.6 


5.7 


3.9 


2 


17 


20.0 


18.4 


17.1 


15.6 


14.5 


13.4 


12.6 


11.8 


11.0 


9.8 


8.1 


6.2 


4.2 




18 


21.2 


19.7 


18.2 


16.5 


15.3 


14.2 


13.3 


12.5 


11.7 


10.4 


8.6 


6.2 


4.6 


1 


19 


22.3 


20.6 


19.2 


17.4 


16.1 


14.8 


14.0 


13.2 


12.3 


11.0 


9.2 


6.7 


4.9 


1 


20 


23.5 


21.7 


20.2 


18.4 


17.0 


15.7 


14.7 


13.9 


13.0 


11,5 


9.7 


7.2 


5.3 




21 


24.6 


22.8 


21.3 


19.3 


17.7 


16.3 


15,3 


14.5 


13.7 


12.2 


10.4 


8.2 


5.8 




22 


25.8 


23.9 


22.3 


20.2 


18.6 


17.1 


16.1 


15.3 


14.5 


12.9 


10.9 


8.6 


6.1 






26 



Original Curves, Tapers Based on Heights above Stump} In the 
form shown, these average taperis or upper diameters may be insufficient 
to bring out the true average form for large numbers of trees. The 
irregularities of form, occasioned by the variation in form of individual 
trees and lack of sufficient number of trees to secure a true average by 
arithmetical means, are best shown b}' i)lotting the forms of the result- 
ant average trees. For this operation, height above stump is taken 
as the independent variable plotted on the horizontal scale while upper 
diameter is the dependent variable plotted on the vertical scale. A 
separate curve is required for trees in each D.B.H. class. 



1 The details of constructing taper curves arc fully discussed by W. B. Barrows, 
Proc. Soc. Am. Foresters, Vol. X, 1915, p. 32. 



METHODS OF CONSTRUCTING TAPER TABLES 



199 



TABLE XXXIV 

Tapers of Loblolly Pine, Two Tkkes 

Tree Class, 15-inch, SO-foot 





Stump 


Height above Stump — Feet 




D.B. H. 


2 


8 


16 


24 


32 


40 


48 


56 


64 72 

1 


Total 
height. 






Diameter inside Bark — Inches 


Feet 


15 4 
15.1 


16.1 
15.0 

31.1 

15.5 


13.51 12.4 
13.3 13.2 


11.4 
12.5 


11.7 
11.9 


11.1 10.0 
10.8 9.6 


8.8 5.9 
8.0 6.3 


3.0 

3.8 


76 

84 


30.5 

Averae,e 

15.2 


26.8 25.6 
13.4 12.8 


23.9 
11.9 


23.6 
11.8 


21.9 
10.9 


19.6 
9.8 


16.8 

8.4 


12.2 
6.1 


6.8 
3.4 


160 
80 



* Data taken from loblolly pine tapers at 8-foot intervals, without stump tapers. Two trees. 



























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32 40 48 56 04 

Height above Stump, Feet 



80 



88 



96 



Fig. 32. — Actual upi)cr dianiotors or tapers of four loblolly pine trees, inside bark, 
based on height above stump, plotted to show form of trees. 90-foot trees. 



200 THE FORM OF TREES AND TAPER TABLES 

From these plotted forms of trees the diameters at any desired point or height 
on the boles can be read. 

The nature of these original averages is shown in Fig. 32 in which four single 
trees of different D.B.H., 14.4 inches, 17.7 inches, 19.4 inches, and 21 inches, but 
falling in the same height class, 90 feet, are plotted. The eccentricities of form 
in this table are partly due to branches, partly to failure to obtain the true average 
diameter at each point, and partly to the natural variations in form for individual 
trees. 

As in the preparation of volume tables, the averages obtained from a number 
of trees are more consistent than the forms of single trees. A graph plotted in 
this manner from averaged upper diameters instead of single trees, will be fairly 
regular in the relation of the curves for successive D.B.H. classes and will resemble 
Fig. 35, p. 204. 

When, as is sometimes the case, the upper diameters are measured 
on logs as cut by the saw crews, in irregular lengths, and hence fall at 
different heights above the stump, only the measurements falling at 
the same height can be averaged, as at 12, 14, 16, 18 and 20 feet. This 
will be done, and all of the resultant upper diameters for trees of a given 
D.B.H. and height class will ])e plotted, to obtain the curve of average 
form. From this curve, the desired upper diameters at regular inter- 
vals of 8 or 10 feet can be read. 

These curves of form are not in final shape for a standard table of form. Although 
the averages are improved by the use of larger numbers of trees, the values will 
be slightly irregular for two reasons. The average D.B.H. may be larger or 
smaller than the e.xact inch class desired, and the forms of the average trees of the 
consecutive D.B.H. classes may vary in fullness. These two sources of variation 
are well shown in Fig. 32. There is no reason why average 21-inch and 18-inch 
trees should have a fuller form than 19-inch trees. 

Values required are based on exact D.B.H. classes, and vary regularly with 
D.B.H., as would be the case were sufficient trees included in the mechanical 
average. 

Second Set of Curves, Tapers Based on D.B.H. For trees of each 
successive D.B.H. class which have the same total height and the same 
general form, the diameters at each given height on the boles will 
diminish in direct proportion with diminishing D.B.H. If D.B.H. is 
then taken as the independent variable in a second set of curves, and 
upper diameters plotted on D.B.H. as the dependent . variable, the 
form of these new curves approaches straight lines as did those of volume 
based on height (§ 141), and the irregularities between the forms or 
upper diameters of different average trees are easily reduced. In this 
second operation as in the first, the trees of a given height class form 
the basis for a set of curves; e.g., 90-foot trees only are included in the 
one set of taper curves, separate sets being rc(iuired for 70-foot or 80-foot 
trees. For this set of curves the same scale can be used for both vari- 
ables, e.g., 2 inches =1 inch. 



METHODS OF CONSTRUCTING TAPER TABLES 



201 



To plot this second set of curves the values for a given tree, or set of tapers, 
are transferred to this new sheet, in which process the strip method described in 
§ 141 is most convenient. 
The diameter of upper 
tapers diminishes with in- 
creasing height ; each tree 
is plotted in a single 
vertical column, with 
the D.B.H. at the top. 

The D.B.H. column 
must be that of the 
actual average D.B.H., 
e.g., 14.4 inches, not 14 
inches. When each set 
of values has been 
transferred and plotted 
above its respective 
D.B.H., the points rep- 
resenting equal heights 
above stump are con- 
nected by lines. The 
guide line for this set 
of curves is a line drawn 
at 45° angle whoso value 
would be D.I.B. = 
D.B.H. For any tree, 
the D.I.B. at D.B.H. 
is less than the D.O.B., 
and at upper points, 
D'l.B. is still less; hence 
all points above D.B.H. 
will fall below this line. 

Regular forms such 
as are shown in Fig. 35 
could be drawn directly 
on Fig. 32 guided by 
the original averages, 
which will usually be 
far more regular in 
themselves than those 
shown in the diagram. 
But the desired shifting 
of the basis to exact 
D.B.H., e.g., 14 inches 
instead of 14.4 inches, 
and the far greater ac- 
curacy in harmonizing 
tapers secured by plot- 
ting (Fig. 33) makes the 
method of plotting a 
second set of curves 
almost obligatory. 




16 17 18 19 
D.B.H., Inches 



20 21 22 



Fig. 33. — Tapers of the four trees shown m Fig. 32, plot- 
ted on basis of D.B.H. for each 8-foot point, and 
results evened off by curves. Separate curves are 
made for each height above stump. Effect is to 
reduce the irregularities of form in Fig. 32. 



202 



THE FORM OF TREES AND TAPER TABLES 



With more regular original averages, the curves will coincide very closely with 
the original data, instead of showing the wide variations indicated in this figure, 
caused by the great irregularity of the original unharmonized values of Fig. 32. 

The effect of this second plotting upon the irregular forms shown in Fig. 32 is 
illustrated in Fig. 35, in which the curved or harmonized tapers from Fig. 33 are 
replotted in the original form.^ 

The values when read from the curves are taken from the ordinates repre- 
senting exact diameter classes. This set of curves therefore is evened off for values 
of the diameter classes, and progresses regularly by 1-inch or 2-inch diameters. 

• Third Set of Curves, Tapers Based on Total Heights of Trees. We 
now have, first, true averages of the original form of each separate 
class, second, true averages for exact diameter classes instead of for 
average diameters larger or smaller than these exact classes. Both 



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Total height of Tree, feet 



90 



Fig. 34. — Tapers based on total heights of trees. For trees of the same 
D.B.H. class. 14-inch trees. 

sets of curves deal, however, only with one separate height class. It 
may happen that the trees of the 80-foot class are all slender, tapering 
trees, while those of the 70-foot or 90-foot class are more cylindrical. 
There is no reason why in a general tabje which seeks average form, 
the accidental departure of form from the average, by a set of trees 
in one height class, should be accepted if this deviation can be easily 
shown and corrected. 

To do this, it is necessary to compare the upper diameters of the 
trees of different height classes, at the same points on the stem. D.B.H. 
must therefore be eliminated as a variable, and height substituted. 



* Since height above stump is the basis of curves in Figs. 32 and 35, the tree 
form is shown as if lying on its side. The diameter, instead of being plotted sym- 
metrically on both sides of an axis, is plotted on the vertical scale above the base 
of the figure. But by holding this figure at right angles, the form of the bole is 
suggested. 



METHODS OF CONSTRUCTING TAPER TABLES 203 

A set of curves (the third) will therefore be made from all trees of 
the same D.B.H., such as the 14-inch class. In this set the independent 
variable which is plotted on the horizontal scale is the total height of 
the tree in feet. The dependent variable is diameter or taper at upper 
points, as in all the graphs used in this method. 

The set of points, which is transferred from curves in Fig. 33 and falls in the 
vertical column above the height of the tree, is the diameter of a 14-inch tree, 
90 feet high, at each taper measurement, the larger diameters, beginning with 
D.B.H., falling highest in the column. 

After each series of points for 14-inch trees, representing trees of different total 
heights as 80, 70, 60 and 50 feet, has been taken from the sejiarate sets of curves 
prepared in step 2, for each of these height classes, and plotted successively on 
Fig. 34, the points representing diameters at the same height, e.g., at 8 feet from 
stump, are connected. 

Irregularities in the resultant curves show departure in form for one height 
class as compared with others. By smoothing out these curves, the tapers of trees 
of different height classes are harmonized. The scale used in this set is 5 feet 
per inch for the horizontal scale, 2 inches per inch for the vertical scale. In Fig. 34 
only the resultant harmonized values are shown 

Fourth Set of Curves, Tapers Replotted on Basis of D.B. H. To utilize 
the data from Fig. 34 the values may be read off direct, forming tables, 
but it is customary to have these tables classified by height classes, 
as in Fig. 33 instead of by diameter classes. To bring together these 
values, the curved values for the separate diameters may again be assem- 
bled on one sheet as in Fig. 33 with a separate sheet for each height, 
diameters on the horizontal scale, upper diameters on the vertical scale, 
and a curve for each fixed height above the stump. This replotting 
should still further iron out any irregularities in taper values. The 
taper table can be read from this set direct, but only for the fixed heights 
given in the table, e.g., for 8, 16, 24 feet, etc. 

Final Set of Curves, Tapers Replotted on Basis of Height above Stump. 
One further step completes the curves of form, by restoring them to 
the shape of the separate trees as shown in Fig. 32. In this final step the 
values are plotted as for Fig. 35, with separate graphs for height classes, 
height above ground on the horizontal scale, upper diameter or tapers 
on the vertical scale and a curve for each diameter class. 

The form of such a set of tapei^ for universal use should be graphic, 
thus showing the upper diameter at every point on the stem. From 
this set of graphs, board-foot volume tables for any log rule, length of 
log, upper diameter limit or stump height, cubic volume, number and 
dimensions of ties, poles or other piece products, can be determined. 
It is apparently a universal basis for the construction of volume tables, 
and while the number and diversity of such tables would remain as 
great as ever, the field work of gathering data on form or volume would 



204 



THE FORM OF TREES AND TAPER TABLES 



be obviated by the printing and general distribution of the graphs 
giving the average form, from which tables could be prepared in the 
office for whatever use was desired. 

169. Limitations of Taper Tables. The real weakness in this 
apparently sound method of preparing the basis for volume tables lies 
in the fact that the result obtained does not differentiate form classes 
of trees, but averages them on exactly the same basis as do the standard 
volume tables. Its only merit therefore is in the transferring of records 



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32 40 48 56 64 

Height above Stump, Feet 



88 



Fig. 35. — Tapers read from Fig. 33 for four diameter classes, showing effect of har- 
monized curves in smoothing out the irregularities of form shown in Fig. 32. 

Similar curves are obtained from tapers rei)lotted inform of Fig. 33 from curves 
shown in Fig. 34. Such tapers will be harmonized by diameter and height classes. 



of average tree forms to the office as a basis for future volume tables. 
The form of the tables is bulky and does not lend itself to the further 
extension necessary to show the form of trees of several different form 
classes for each diameter and height class, though in the preparation 
of standard volume tables by the U. S. Forest Service, such taper tables 
have been extensively employed. The use of taper tables in connec- 
tion with standard form classes as a basis for universal volume tables 
is discussed in Chapter XVI. 

By preparing separate sets of taper tables for each form class based 
on absolute or normal form of trees (§ 174) a permanent basic standard 
of tree form is obtained which will fill all possible future requirements. 



CHAPTER XVI 
FORM CLASSES AND FORM FACTORS 

170. The Need for Form Classes in Volume Tables. Trees which 
have the same D.B.H. and total height may vary in form, as shown, 
according as the tree is full boled, with " good " form, or concave 
boled, with " bad " form. These gradations of form correspond with 
differences in cubic volume. In order to further classify the volumes 
of trees of the same D.B.H. and height, tliis range of volume due 
solely to form must be separated into arbitrary classes or divisions. 
Such a series is based on measurable differences in form, and the 
classes thus established are termed fonn classes. The adoption of 
form classes as a third variable in constructing volume tables has 
been retarded in this country by the necessity for expressing volumes 
in terms of board feet, by the labor of constructing even the simpler 
tables based on diameter and height, and by the belief that the vari- 
ations due to form could be more simply overcome by averaging them. 

A second difficulty lay in the application of such form-class tables 
in timber estimating, since cruisers were unaccustomed to judging 
upper diameters by eye with the accuracy needed to distinguish between 
the form classes. Differences in taper were readily recognized, but 
differences in form were further obscured by the method of using 
merchantable top diameter limits instead of total height. Practical 
cruising did not seem to require such tables. But with the increasing 
use of the cubic foot and the cord for pulpwood and in second-growth 
timber, and the need for closer estimating, the desirability of distinguish- 
ing form classes in volume tables is increasing. Such efforts as have 
been made so far in this country follow standards prevailing in Europe, 
where the universal use of the cubic unit, close utilization and high 
values have made it necessary and possible to obtain more accurate 
measurements of the standing timber. 

One great possibility in this field is the demonstration that when 
form classes are distinguished and the true form of the tree inside the 
bark is made the basis, all species of trees will be shown to have practi- 
cally the same forms and total volumes for the same form classes; hence 
a single general table so classified would suffice for all field work. Were 
this fact established, a basic table might then be constructed for each 

205 



206 FORM CLASSES AND FORM FACTORS 

of various units of measure in addition to cubic feet. Once the average 
form class of the trees or stand were determined, then volumes could 
be obtained from these basic tables. Recent research in Sweden tends 
to show that this generalization holds true for certain species already 
investigated, namely spruce, fir, larch and Scotch pine. 

171. Form Quotient as the Basis of Form Classes. The first real 
step towards a solution of this problem was made by Schiffel in 1899, 
who developed a method of expressing differences in form, previously 
used (Schuberg, 1891) and known as the form quotient, which is the 
percentage relation that the diameter at one-half the height bears to 
the D.B.H. 

The differences in form of the entire boles of trees (Chapter III) 
are expressed by their divergence from a cylindrical form through a 
series marked at definite stages by the complete paraboloid, cone, and 
neiloid. Each of these solids can be measured by Newton's formula: 

F=(B+46.+6)| 

The middle point on the stem of a tree, regarding the entire bole as a 
single complete solid, is evidently the point of greatest weight in deter- 
mining its form and volume with respect to the cylinder whose base is 
B and height h. 

By a complicated calculation, - Schiffei derives tne formula for 
obtaining at one operation the true cubic contents of an entire stem as, 

F=(.165+.666,.)/i. 

This is known as Schiffel's formula. 

Newton's formula, regarding the tree as a perfect, i.e., complete 
conoid, and the diameter at top as zero would be, 

F=(.16fB+.66|6.)/i. 

The " universal " character of Schiffel's formula failed to make the 
headway expected when it was first introduced in the United States 
for the reasons that, to apply it, one must measure the diameters of 
trees at one-half the stem height, and that the cubic unit of volume 
was little in demand. 

The really valuable part of Schiffel's work was not the formula, 
which was nothing new, but the form quotient. This was his demon- 
stration that the true form, and consequently the variation in form of 

1 "New Method of Measuring Conifers," Review by B. E. Fernow of Article 
by SchifTel, "tjber die Kubirung und Sortierung Stehender Nadelholz Schafter," 
Centralblatt flir das gosammte Forstwesen, Dec, 1906, pp. 493-505, Forestry Quar- 
terly, Vol. V, 1907, p 29. 



FORM QUOTIENT AS THE BASIS OF FORM CLASSES 



207 



different trees, could be indicated by the relation between diameter at 
one-half height and D.B.H. (not diameter at stump). 
In its standard form of expression: 

Form quotient = — . 

In 1908 Tor Jonson corrected a slight inconsistency in Schiffel's 
method by insisting that the middle diameter be taken not at the middle 
point of the stem but at the middle point measuring from B.H. This he 
termed the absolute form quotient. This improvement finally secured a 
consistent basis for expressing tree forms, eliminated height as a varia- 
ble, and got rid of the great drawback of butt swelling. The absolute 
form quotients of trees were now found to vary between .575 and 
.825, i.e., the diameter at the middle point above B.H. bore this 
relation to the D.B.H., whether both measurements were taken out- 
side or inside the bark. 

It was also discovered that in most cases the form quotient if reduced by a 
constant would give the form factor for cubic contents of the tree. For instance, 
J. F. Clark found that the reduction factor for the form quotients for balsam in the 
Adirondacks was 0.21. This fact is of minor importance since it aids only in 
obtaining the cubic contents of trees. 

This standard of measuring form permitted the classification or 
differentiation of the third variable of volume, namely, form independ- 
ent of diameter or of height. Trees could be grouped into form classes 
expressed by form quotients. Seven main form classes were formed, 
namely, .50, .55, .60, .65, .70, .75, .80. Five sub-classes were also inter- 
polated as .575, 625, .675, .725, .775. The extreme lower and upper 
classes shown will be found only in individual trees. The average 
form class for a given stand will fall usually between .575 and .75 and 
may be correlated with the density of the stand as shown below. 



Character of stand 


Form class, 

based on 

form quotient * 


Poor density 

Fairly good density 

Good density 


0.575-0,625 
.65 

.675- .70 
.725- .75 


Overcrowded 



* Tor Jonson, 1918. 



But most important of all, the question as to whether the form of 
trees was independent of species, site and region and dependent on gen- 
eral laws, could now be determined. 



208 FORM CLASSES AND FORM FACTORS 

172. Resistance to Wind Pressure as the Determining Factor of 
Tree Form. The theory cxphiiniiig the form of the boles of trees, 
v/hich is now generally accepted, was first advanced by Prof. C. 
Metzger, a German. This was, that the stem or bole is constructed 
as a girder to withstand the pressure of wind. Based on this theory, 
A. G. Hoejer, a civil engineer of Stockholm, devised the general formula 
for tree form discussed in § 173. Prof. Tor Jonson applied this 
formula first to spruce and then to Scotch pine, and demonstrated its 
correctness; as a consequence, developing the basis for tables of abso- 
lute form and volume for trees, and a new method of estimating 
thnber (§ 203). 

Jonson's conclusions, based on these investigations, are that tree 
form depends entirely on the mechanical stresses to which the tree is 
exposed, and is therefore independent of diameter, and height, and also 
of species, age, site or any other factor, except as these factors in- 
fluence the form of the crown. The force of the wind operates on 
the crown of the tree and is focused or centered on a point representing 
the geometric center of the crown. The pressure of the wind on the 
tree crown constitutes a force which compels the tree to construct its 
stem in such a manner that the same relative resistance to strain is 
found at all points, the smallest possil)le amount of material being 
used. As the concentrated force of the wind strikes a point situated 
lower or higher on the tree, dependent on the crown area presented, 
we get larger or smaller taper respectively, which means bad or 
good form class. As the location of the point of attack of the bend- 
ing force is determinative of form, this point is called the form point, 
and can be expressed as a per cent of total height. 

Here is a natural law, to which growth of trees, as mechanical struc- 
tures designed to stand up against wind, corresponds. The full bole 
of the forest-grown tree in a crowded stand, coinciding with a small 
crown and high form point, meant that this location of the strain 
required nearly equal strength along the total length of bole, which 
could be attained by rapid growth of the upper bole. If the tree 
were open-grown with a consequent long crown and a low form point, 
this would permit of smaller upper diameters and require greater 
strength lower down on the bole. 

Since the form of the crown, especially its length, with relation 
to the length of bole, determines this form point, this relation of crown 
to bole, expressed by form point serves as an index to classify trees as 
to their relative form classes or form quotients. 

Any variation in average form, such as the admitted fact that the 
average form quotient increases with age, is explained by a coincident 
change in this crown and form point relationship. Open-grown trees 



A GENERAL FORMULA FOR TREE FORM 209 

possess a low form quotient, not because they are open-grown but 
because the crowns of such trees are long and the form point low. Trees 
with long clear length and high crowns possess a high form quotient, 
whether they stand alone or in a crowded stand. Short trees may be 
full-boled or the reverse — the rapidity of taper as a whole has no effect, 
but the distribution of the taper, which alone affects the form quotient, 
will vary with short trees as much as with tall, and on poor soils equally 
with good. 

173. A General Formula for Tree Form. On this basis, if the actual 
form of trees with the same form quotient is similar, it would be possil)le 
to construct taper tables based on each of the three variables, diameter, 
height and form class, which would apply to all species of trees. To 
apply this principle there was required a general formula which would 
give the diameter of a tree of given form quotient, at any point on the 
stem, and second, a demonstration that the actual measurements taken 
on trees of this form quotient coincided with the results of the formula. 

Once this was shown, the formula would permit of the construction 
of a set of taper tables of universal application from which in turn any 
manner of volume table could be derived. This is a more ambitious 
program than the mere determination of form factors for cubic con- 
tents, and promises permanent results. 

The formula devised by A. G. Hoejer is based on the portion of the tree 
above B.H.: 

D = D.B.H. inside bark; 
Z = distance from top of tree to section; 
d = diameter of section. 

Then 

d c+l 

D c 

C and c are constants whose value depends upon the form quotient of the tree; 

d 
i.e., upon ■- when d is measured at one-half height above D. Their value must be 

found separately for each form class, and will then hold good for diameters at any 
point on the bole of trees within this class, independent of total height of tree. 

Absolute heights are not used in the formula, but percentage or relative heights, 
regarding the height of any tree above B.H. as 100, and the distance below the 
tip, of any other section as its per cent of this length, including sections below 
B.H., whose per cent of height would exceed 100. 

In the same way, absolute diameters are not used, but the D.B.H. is taken as 

d 
100, and the relative diameter — expressed as its proportion of 100. 

These upper diameters are then measured at distances equaling tenths of this 
total height above D.B.H, — thus falUng at the same proportional height on each 



210 FORM CLASSES AND FORM FACTORS 

tree; e.g., for the form class 0.70 with diameter at 0.5 of height above B.H., asJ 
0.7 of D.B.H., the values in the formula are: 



For upper section, 



For D.B.H. section, 



70 ^, c+50 
= Clog-^- 1) 

100 ^ c ^ ^ 



100 c + 100 

=Clog-^ (2) 

100 ^ c ^ ^ 

If equation (2) is divided into equation (1), then 

0.70 log (f + 100)=log (r+50) + (0.70-l) log C. 

The value of this constant c is then found by trial. Inserting this value in equa- 
tion (2) the value for constant C is found for the form class. Values for the remain- 
ing form classes are found in a similar manner. 

With the numerical value of the constants C and c determined, the normal diam- 
eter of a perfectly formed tree can be found by this formula at any point on the 
stem above B.H., and this normal diameter can also be calculated for stump height, 
thus disregarding the stump taper. 

By determining these normal diameters for trees of each D.B.H. and height 
class, at intervals of one-tenth of the total height, and plotting these diameters 
graphically, a set of taper curves is constructed (§ 167), for normal tree forms, 
from which volume tables or form factors can be constructed which will have 
universal application. 

174. Applicability of Hoejer's Formula in Determining Tree Forms. There 
remained to test accuracy of these results by comparing them with measurements 
on felled trees. The tests showed that for the conifers measured, spruce, fir, larch 
and pine, the formula expressed the form of the living tree, when applied inside 
the bark at all points including D.B.H., and that for species with thin bark such 
as spruce, the same relations applied when measured outside bark. For Norway 
Spruce the volumes of individual trees fall within =b 3 per cent of those derived 
by the formula. But for thick-barked species such as Scotch pine, a poorer form, 
less cylindrical, was obtained outside bark, which changed the form class, but 
did not seriously interfere with the application of the method. Claughton- 
Wallin has since shown that this formula holds good for Norway or red pine 
{Pinus resinosa) and white pine (Pinus strobtis). 

As with all attempts to study the laws of tree form, this formula depends on 
measuring a diameter which is not affected by the abnormal flare at the butt; 
hence any tree or species whose butt swelling extends above B.H. will not corre- 
spond in form to the diameters in the formula based on this abnormal D.B.H. 
It was found impossible to use the formula for western conifers since the form 

d 
quotient — was too low for this reason. 

For general application, the second difficulty is the factor of bark thickness, 
whose effect upon the form quotient and form class must be worked out for different 
species with variable thicknesses of bark, so as to correlate the method with D.B.H. 
measurements outside the bark, which must continue to be used in practical 
estimating. 



FORM FACTORS 211 

Can these two variables be eliminated for American trees, and taper and volume 
tables constructed for trees of each form class, thus attaining the goal of universal 
volume tables? 

For second-growth, or young timber, in which the factor of butt swelling will 
not affect D.B.H., this can be done. Taper tables should be constructed from this 
normal formula based on diameter inside bark at B.H. The average thickness of 
bark at B.H. must be determined for the species, and by graphic interpolation 
these D.I.B.^aper tables can be drawn for trees of each D.B.H. outside bark, from 
which volume tables can be constructed in any desired miit. 

For the larger trees or species with butt swelling extending above B.H., as for 
instance, virgin stands of timber on the Pacific Coast, or Southern cypress, the 
present practice of adhering to D.B.H. will probably be continued, and trees with 
variable amoimts of stump taper averaged together in volume tables regardless of 
true form. The only alternative is to attempt a standard measurement of diameter 
at a higher point on the bole, which will be difficult to adhere to in practice. Approx- 
imate rather than absolute accuracy will continue in the preparation and use of 
these tables for such timber. 

When the variable influence of butt swelling is further aggravated by the 
obsolete practice of basing volume tables on diameter at the stump, no consistent 
volumes can be obtained to serve as standards for estimating. 

175. Form Factors. The form of a tree is a variable independent 
of diameter or height, while the form of a cylinder does not vary at all. 
That of a cone is a constant, equal to one-thii'd of the volume of a 
cylinder of similar height. Taking the volume of a cylinder as the 
unit of comparison, and dividing the volume of a cone by that of the 
cylinder of equal diameter and height, the quotient is always .333 or 
one-third. This can be termed the form factor of this cone, i.e., the 
factor by which the volume of the cone is derived from that of the cylin- 
der. It expresses the volume of the cone, but not its form. In the same 
way the form factor of the paraboloid is .5. 

Form factors of trees can thus be found by dividing their cubic 
volume by that of a cylinder of equal diameter and height. 

5 = Basal area of cylinder equivalent to that of tree; 
/i = height of cylinder and of tree; 
Bh = volume of cylinder; 
/=form factor or multiple expressing the relative volume of the 

tree; 
V = volume of tree. 

Then 

Bh 

J y , 



and 



V=Bhf. 



212 FORM CLASSES AND FORM FACTORS 

Volumes of trees can thus be obtained from the vokuiies of cyHnders, 
when once the average form factor is known. 

The form factor is therefore, in theory, a direct expression of the 
relative volume of a tree compared with a standard or constant volume, 
and tables of such factors were expected to give the key to universal 
volume tables showing form classes. But the diameter of the cylinder 
which is to serve as the unit or basic volume must first be obtained and 
must equal that of the tree. If this diameter is taken at the stump or 
at ground, the butt swelling gives an abnormally large irregular vari- 
ation in the cylindrical volume. This method is known as the Absolute 
Form Factor. 

But the diameter can be shifted to B. H. with the cylinder equaling 
the total height of tree as before. Form factors so calculated give uniform 
or consistent results from which cubic volumes can be calculated, 
and are termed Breast-high Form Factors. These form factors in turn 
vary not only with the form of the tree, but with the total height as 
well, hence could not be used to indicate absolute form. The reason 
is that the diameter of the basic cylinder is taken, not at a height pro- 
portional to the total height of the tree, but at the fixed height of 4^ 
feet. For short trees this point falls proportionally nearer the tip, 
with relatively smaller cjdinder, than for tall trees of identical form. 
The breast-high form factor therefore decreases as height of tree 
increases. 

In an effort to overcome this drawback and express form directly 
by means of form factors, the so-called Normal Form Factor was devised, 
in which the basal area is measured at a point on each tree represent- 
ing a fixed ratio to the height of the tree. This plan has not proved 
pi'actical, owing to the difficulty of determining this point rapidly and 
accm-ately. 

By comparing only the portion of the tree above B.H. with the 
volume of a cylinder of equal height, the form factor for this portion 
alone corresponds dii'ectly with variations in form for the tree. This 
is known as Riniker^s Absolute Form Factor. 

The Riniker form factor of trees of each form class was calculated by Jonson 
from the normal form or tapers of trees of each D.B.H. and height class, taking 
the diameters at points representing one-tenth of the stem above B.H. Then 

V 

f = — for the bole above B.H. only. 
■' Bh 

Since form quotients indicate correctly the relative forms of trees, absolute 
form factors of trees whose form quotients are equal should also be equal. That 
this is true is indicated by the following test, e.g., from investigations of Claughton- 
Wallin and F. McVicker: 



STANDARD BREAST-HIGH FORM FACTORS 



213 



Species 


Form 
quotient 


Cubic 
form factor 


Basis 
trees 


Red pine, Ontario, Can 

Scotch pine, Sweden 

Red pine, Ontario, Can .■ 

Scotch pine, Sweden 

Red pine, Ontario, Can 

Scotch pine, Sweden 

White i)ino, Ontario, Can 

Scotch pine, Sweden 

White spruce, Ontario, Can 

Scotch pine, Sweden 


65 
65 

70.3 
70.3 

74.4 
74.4 

70.8 
70.8 

65.2 
65.2 


0.439 
.441 

.480 

.484 

. 515 
.524 

.482 
.489 

.441 
.444 


11 

30 

40 

9 

6 



176. The Derivation of Standard Breast-high Form Factors. The 

two possible uses for form factors are seen to be, first, an expression of 
relative forms of trees, second, a means of computing their total vol- 
umes from that of cylinders. 

It is not possible to combine these two functions in the same table 
of form factors. The absolute form factors for total tree volume can- 
not be correlated with D.B.H. nor with any other point on the bole, 
while the form factors which are based upon D.B.H. and total volume 
are not absolute but vary with height. But these Riniker's absolute 
form factors can be used to obtain a set of breast-high form factors 
which represent the relative volumes of normally formed trees of all 
diameters and heights when compared with the corresponding cylinders. 

The steps in this calculation are: 

1 . Compute the Riniker form factor for trees of each form class. 

2. Obtain the normal stump diameter from Hoejer's formula. Stumps were 
taken as 1 per cent of the height of the tree. The actual stump diameter is always 
too large, due to butt swelling. The conception of a normal stump diameter is 
the diameter which the stump would have if the normal curve of the stem from 
top to D.B.H. were prolonged downward to stump height. 

3. Find the diameter at one-half the distance from stump to top, by Hoejer's 
formula. 

4. Express both the stump diameter and the diameter at one-half height in 
per cent of D.B.H. and compute the new form quotient, this time based on height 
above stump. 

If diameter at ^t =67.7 per cent of D.B.H. 

Stump diameter =103.0 per cent of D.B.H. 

67.7 



Form quotient 



103.0 



= 0.657. 



214 FORM CLASSES AND FORM FACTORS 

5. From the table of absolute form factors interpolate for the form factor required 
to coincide with this form quotient.' 

6. The basal area corres{)onding to the normal diameter at the stump is found 
as follows: 

Do = normal stump diameter; 

Z) = D.B.H.; 

Bo = normal basal area at stump; 
B = basal area at D.B.H. 
If 



Do 


^l.OpD, 


Do= 


= 1.0lf-D^, 


Bo 


ttDo^ 

4 




xD2 
4 



= 1.0pW. 

7. Total volume of the stem is then 

V = BJ,f, 
= B l.OpVifo. 

8. Breast-high form factor is 

^^Bh 
= 1.0p%. 

This series of breast-high form factors shows the diminution with increased 
height, the cause of which is set forth in § 175. These form factors are given in 
Table LXXXII, Appendix C, p. 497. 

Since form is best shown by taper tables, and volume is best obtained 
directly from volume tables, the use of form factors in America has 
but little practical application and has been adopted to a very limited 
extent. Were the breast-high form factors more regular they would 
serve as a means of constructing volume tables by graphic methods 
(§ 138) in which the curves being comparatively straight could be 
extended and interpolated with less chance for error than by the ordi- 
nary methods. 

177. Merchantable Form Factors. Form factors based on the 
merchantable contents of the tree in cubic feet, or upon the net cubic 

1 These absolute form factors are for the entire tree, but are based on the 
theoretical stump diameter, hence are inapplicable for practical use. 



FORM CLASSES AND UNIVERSAL VOLUME TABLES 



215 



volume utilized as board feet or in any other unit, can be computed 
by first ascertaining this net volume. The form factor is 



/= 



Bh 
V 



These form factors serve no useful purpose. 

178. Form Height. Form height is the product of form times 
height. 

Since V=Bhf, tables of form height simply eliminate one of the 
two multiplications necessary in deriving cubic volumes. 

0.710 

0.G90 

0.G70 

0.G50 

0.630 

O.GIO 
5 0.590 
I 0.570 

g 0.550 

o 

^ 0.530 
u 

I 0.490 
0,470 
0.450 
0.430 
0.410 
0.390 
0.370 



n 



0.350 











































\ 








































s\ 






































v\~ 






































^ 




\ 


^ 




^ 








For 


Ik 


lass 


















^N 


fx 


V 




-«.. 


.^ 








-~\ 


■ — 


— 


— 














^ 


:n 


\ 




^ 








—■ 


— — . 


ojrhj 


.^^ 
















^N^ 


\ 




r^ 








^ 




Qjl 


















|;^\: 


\ 


^ 


k 








— . 




0.725 










— 










N 


^ 




■ 











0.7f 






■ — 


— 






















N\ 


\ 




^ 


"^ 






. 




O.pf 


fl^ 


' 


1 







— 












s 




'^ 
















■ 


1 




-J 




- 






^ 


^^ 


K 


"^ 


^ 






>^ 




■^1 













. 










^ 


'^ 


\ 


^ 

>> 


^ 






^ 




0,60^ 


























■^ 


<^ 


V 


^ 






^ 




2:575 


































X 


"^ 








0^ 

0r52 

2i5C 


1 


__^ 








■ 
























. 




^ 








. ^ 
































-r 


■ — 


— 





1 












20 25 30 35 40 15 50 55 60 05 70 75 80 
Heiglit in Feet 



85 90 »5 100105110115120 



Fig. 36. — Curves of breast-high form factors for form classes from .50 to .80 inclu- 
sive, showing effect of height ui)on the form factor. From Tor Jonson. 

179. Form Classes and Universal Volume Tables as Applied to 
Conditions in America. The standard form classes, when applied to 
trees of different diameter and height, thus distinguish three variables 
just as did the universal volume tables based on diameter, merchant- 
able length and rate of taper. Universal volume tables if based on 
total heights would show volumes for the given unit in three instead 
of two dimensions; D.B.H., Height, Form Class. 

But to derive universal volume tables by form classes to be based 
on merchantable length instead of total height would not be so simple, 
for the following reasons: 



216 



FORM CLASSES AND FORM FACTORS 



72 ft. 



If taken to a uniform or fixed top diameter, trees with a high form 
quotient would be cut higher in the top and fall into a different merchant- 
able height class than trees with a low form quotient. Therefore, for 
trees of different form quotients, to attain the same merchantable top 
diameter, trees with the lower quotients must be taller than those whose 
form quotient is high. Hence total and merchantable heights are 
not interchangeable for trees whose form quotients differ. 

If taken to variable top diameters, this second variable will make 
it practically impossible to distinguish form classes based on total 

height in the volumes 
given, for these tops 
would not vary in any 
definite relation to 
total height or form. 

As long as mer- 
chantable rather than 
total heights arc used 
in volume tables and 
timber estimating, 
form classes based on 
actual form of the 
tree cannot be used 
to construct volume 
Fig. 37. — Effect of cutting to a fixed top diameter, upon foKlgg \i^ which trees 
merchantable height of trees having different form . ,.™ . „ 

,. , . r ^- ,. e rn .n ot dmereut iorm are 

quotients. A form quotient ot .60 requires either a 

shorter merchantable length or a taller tree than one separated, and tne 
of .80. principle of averaging 

the differences in vol- 
ume due to form must continue to be used for such tables. 

But for cubic feet, basic volume tables may be made up giving the 
volume of each diameter, height and form class. Similar tables can be 
constructed in any unit of volume, or for any log rule, from tables of 
normal taper. In applying these tables, the method would be not to 
attempt to tally each tree in its proper form class, but to determine 
average form classes (§ 171) for stands or other subdivisions of the 
forest, the volumes for which can be taken from this basic table to form 
a standard volume table for the trees to which it applies. Not over 
three such tables would be apt to be needed for any tract, however 
large and varied. 

Methods of rapidly determining the form class of sample trees, in 
order to apply such a system, are given in § 201, § 202 and § 203. 




REFERENCES 217 



References 

New Method of Measuring Volumes of Conifers, Review of Schiffel's method by 

B. E. Fernow, Forestry Quarterly, Vol. V, 1907, p. 29. 
Das Gesetz des Inholts der Baum Stiimme. Forstwissenschaftliches Centralblatt, 

Aug., 1912, pp. 397-419. 
Massatabellar fiir Traduppskattnung, Tor Jonson, Stockholm, Sweden, 1918. 

Review, Forestry Quarterly, Vol. XI, 1913, p. 399. 
Article by L. Mattson-Marne,Skogsverdsf6reningensTidskirft, Feb., 1917, pp. 201-36. 
Form Variations of Larch, L. Mattson-Marne, Meddelanden frau Statens Skogsfor- 

soksanstalt, 1917, pp. 843-922; Review, Journal of Forestry, Vol. XVI, 1918, 

p. 725. 
The Absolute Form Quotient, H. Claughton-Wallin, Journal of Forestry, Vol. XVI, 

1918, p. 523. 
Tor Jonson, "Absolute Form Quotient" as an Expression of Taper, H. Claughton- 

• Wallin and F. McVicker, Journal of Forestry, Vol. XVIII, 1920, p. 346. 
Die Formausbildung der Baumstamme, Von Guttenberg, Oesterreichische Viertel- 

jahrschrift fiir Forstwesen, 1915, p. 217; Review, Forestry Quarterly, Vol. 

XIV, 1916, p. 114. 



CHAPTER XVII 

FRUSTUM FORM FACTORS FOR MERCHANTABLE CONTENTS 

IN BOARD FEET 

180. The Principle of the Frustum Form Factor. In an effort to 
simplify the construction and improve the accuracy of volume tables 
for board feet based upon merchantable heights and top diameters, 
a merchantable form factor has been devised by Donald Bruce. 

Timber cruisers in the Pacific Northwest had already made use 
of the similarity in form of the merchantable portion of the tree to that 
of the frustum of a cone, but had neglected the possible differences in 
form and volume between the cone and the merchantable bole. The new 
method adopts the frustum of the cone as the basic volume, instead of 
the cylinder as for the form factors discussed in Chapter XVI, and then 
compares this volume with that of the tree, to determine their true 
relation. This relation is expressed as a form factor in the usual manner. 

y = volume in tree; 

y' = volume in frustum of cone; 

/=form factor. 
Then 

and 

The contents of this frustum were measured as the scaled board- 
foot contents of cylindc^-s representing the logs into which the bole 
would be cut. The length of these sections was fixed at IG feet, and 
their upper diameters were determined by the diameter of the frustum 
at the required point. The form factor obtained by comparing the 
total scaled volume of the merchantable bole with that of the frustum 
so measured is termed the Frustiun Form Factor and is a merchantable 
form factor having values close to 1, since the deductions from full 
cubic contents of bole have been made both in the frustum and in the 
tree. 

The merits of the frustum form factor method for constructing 
volume tables are that it applies directly to the merchantable portion 

21S 



BASIS OF DETERMINING DIMENSIONS OF THE FRUSTUM 219 



of the tree, on the same basis as used in timber estimating to top 
diameters, and that the vahies of the form factors tend to vary but httle 
from a straight hne, thus permitting the construction of curves of board- 
foot volume with greater accuracy than when volumes are plotted 
directly (§ 138). This advantage permits of constructing such tables 
on the basis of fewer measurements of felled trees. 

181. Basis of Determining Dimensions of the Frustum. The top 
diameter of the frustum is supposed to coincide with the top diameter 
inside bark of the merchantable length of each tree class. The diam- 
eter at its base, which is at stump height is arbitrarily fixed as equal 
to D.B.H. outside bark. No pretense is made that this form factor 
is a scientific basis for studying tree form. Actual D.I.B. at stump 
may or may not coincide with D.B.H. outside bark. The base of the 
cone must be correlated with D.B.H. rather than with stump diam- 
eters (§ 175) and this assumption is satisfactory. 

Since the sides of a cone are straight, the upper diameters of each 
" log," or standard length into which this frustum is divided, are 
determined by proportion, to the nearest iV inch. 

In calculating the volumes of the frustums of cones the determination of the 
diameter at the top of each successive 16-foot log for cones of different top and 
base dimensions is best per- 
formed by plotting the form 
of the cone on cross-section 
paper, on which the vertical 
scale shows diameters and the 
horizontal scale shows heights 
in feet. Plot, first, D.I.B. 
equals D.B.H. at zero or 
stump height; next, top diam- 
eter inside bark at the mer- 
chantable height. Connect 
these two points by a straight 
line representing the side of Fig- 38.— Method of plotting a frustum from 
the frustum. The diameters which to determine the top diameters of the 
inside bark at top of each log l"gs which it contains, 
are then read at 16 feet, 32 

feet, etc., to the nearest yo inch. The log rule should be tabulated to show the 
values for each ro inch. 

182. Character and Utility of Frustum Form Factors. That the frustum form 
factor is a practical rather than a scientific basis of measurement is shown by the 
following facts: The absolute form factor of the total contents of the bole (§ 175) 
would be 0.5 when the tree has the form of a paraboloid. A truncated portion of 
the bole, with the rapidly tapering top eliminated, when compared with a trun- 
cated cone having the same top diameter, represents the lower portion of a cone 
of considerably greater height than that of the tree or paraboloid. 

For cone and paraboloid (or tree) of equal total height, the form factor of the 

5 
tree, compared with the cone is — or 1.50, since 0.5 and 0.33 are the respective 



20 



/•■' 


B. atb 


ise=D 


.B.H.2 


0" 










~~~" 


^-^ 


^^ 




















"" 


^^ 






















^ 


8Top 



















16 



32 40 
Feet 



220 FRUSTUM FORM FACTORS 

volume form factors of the paraboloid and cone when compared with a cy Under of 
equal dimensions. 

The nearer the top of the tree this upper diameter falls, or the closer the degree 
of utilization, the shorter will the completed cone become, until it coincides with 
the paraboloid in height. In the same manner the frustum form factor will increase, 
until it reaches a maximum of 1.50 for the completed cone. 

Chandler, 1 in an extensive investigation of the frustum form factor of northern 
hardwoods, birch, beech and maple, determined that this factor was independent of 
species, site or other influences, and independent of diameter and height, but was 
dependent on the two factors, form quotient, and taper ratio. The form quotient 
agrees in principle with that of Tor Jonson. Based on D.B.H., instead of stump, 
it was computed for merchantable rather than total height, by first subtracting 
diameter at top or d from both diameter at B.H. and at middle of merchantable 
length. Then 

d-i — d 

The taper ratio is the ratio between top diameter of merchantable bole, and 
D.B.H. 

Merchantable cubic frustum form factors were found to diminish as form 
quotient diminished and as taper ratio increased. The first result is obvious. 
The second confirm^ the conclusions set forth above as to the effect of close utiliza- 
tion in increasing the frustum form factor. 

These researches have definitely proved, on an empirical basis, the fact that, 
other things being equal, frustum form factors based on a fixed top diameter do 
not express a scientific relation between the form and volume, but will vary with 
the relation between cone and paraboloid. In its final analysis, the frustum form 
factor is an endeavor to express the paraboloidal forms of trees by the use of frustums 
of cones and the application of a correction or form factor. Although a great 
improvement over older methods if intelligently applied, it is not a universal 
method, since its results vary with taper ratio, butt swelling, bark thickness, and the 
top diameter utilized. 

On the other hand, the natural divergence in the total form and cubic volume 
of trees which gives rise to the variation m form quotients of from 0.575 to 0.8 is 
overcome in a marked degree by the substitution of the merchantable frustum 
form factor since, first, trees with a high-form quotient and of the same total height 
will be cut higher in the tops than those with a low-form quotient (§ 179). The 
merchantable form factor in itself coincides with this greater utilization and there- 
fore approaches closer to vmity, for both forms. If all trees are utilized to a fixed 
top diameter, a cylindrical tree, being cut nearer to its tip than a conical tree, 
would have fallen into a larger total height class than the conical tree, hence its 
per cent of cylindrical contents would have been much greater for merchantable 
form factor than that of the conical tree — a difference not appearing in the frustum 
form factor. Second, where the actual top diameter is made to coincide with the 
point at which the tree is commonly utilized instead of with a fixed top, there is apt 
to be still closer approach to unity in the form factors. The length and character 
of the crown usually determines the amoimt of taper from the base of the crown 
to the tip of the tree and consequently its distribution on the stem (§ 172). In 
rough utilization, the last saw cut tends to bear a direct relation to the length of 
crown and to fall nearer to the base of the crown than to its tip. This is especially 

1 Bui. 210, Vermont Agr. Exp. Sta. 1918. 



CALCULATION OF THE FRUSTUM FORM FACTOR 221 

true of hardwoods with branching crowns. Measured from this point, the frustum 
of the tree will not differ greatly from that of either a cone or a paraboloid. 

A great source of irregularity in frustum form factors, as in absolute form factors 
for cubic contents, is found to be the influence of butt swelling extending above 
B.H. and second, the influence of thickness of bark. Both of these factors reduce 
the proportion of woody contents to the dimensions and consequently reduce the 
form factor. 

183. Calculation of the True Frustum Form Factor. A far more 
serious difficulty in the use of the frustum form factor hes in securing 
the exact coincidence of the top diameters of the frustums, used as the 
unit or standard for volume, and the average top diameters of the trees 
whose volumes are to be compared for the determination of the form 
factors. There is but one exact method, namely to compute the form 
factors of a given height separately for each tree whose D.B.H. and 
top diameter differ even by yVinch, by using a frustum whose three 
dimensions exactly coincide with those of the tree frustum. This 
method gives the most consistent form factors. The results for long- 
leaf pine given in the table on p. 222 were obtained by this method. 

This method can be simplified by first averaging together for all 
the trees in a diameter and height class the four factors, volume, D.B.H. , 
height, and top diameter. The frustum of a cone having these aver- 
age dimensions is then used to determine the frustum form factor of 
the class, by comparing its volume with that of the average tree of 
the class. While less accurate, this method reduces the computations 
considerably and is within the required limits of accuracy of the method. 

By this method, the computation of the frustum form factors is 
the first step in the construction of the volume table for which they 
are intended. 

184. Calculation of the Volumes of Frustums. Influence of Fixed 
versus Variable Top Diameters. The purpose of the frustum form 
factors thus obtained is to make possible the construction of a volume 
table in board feet, by applying these factors to the volumes of frustums 
of cones. This may be done in the office, once the factors are known 
and the dimensions of the frustums determined. 

The second step is therefore to determine these dimensions of frus- 
tums of cones. The base is fixed, being equal to D.B.H., in 1- or 2-inch 
classes. But the top diameter of these cones is a source of trouble. 
As seen in the construction of volume tables (§§ 157-158) the top diam- 
eters to which trees are actually utilized tends to decrease as height 
increases, and to increase with D.B.H. The table will be based on 
one of two plans, a fixed top diameter, or variable top diameters coin- 
ciding with actual utilization. 

Whichever basis is adopted, the top diameters of the frustums 
must coincide with the average top diameter of the merchantable boles, 



222 



FRUSTUM FORM FACTORS 



whose volume is sought. If frustums having a fixed top diameter 
Hmit are used, the form factors should have been computed from trees 
measured to this same top diameter. If on the other hand, an attempt 
is made to base the table on variable or actual used top diameters, then 
the average actual top diameter for each diameter and height class 
should first be found and the frustum having the requisite top dimen- 
sion for each class computed. 

TABLE XXXV 

True Frustum Form Factors for Longleaf Pine, from Frustums Whose Top 
Diameters Coincide Exactly with the Average Top Diameter of Trees 
of Each D.B.H. and Height Class 

Merchantable Length in 16-foot Logs 



D.B.H. 


2 


2\ 


3 


31 


4 


4i 
4. 


Averaged by 
diameter, 
Weighted 


Inches 


Frustum Form Factors 


12 


0.98 


0.98 










0.980 


13 


.97 


1.21 


0.99 








.992 


14 


.96 


.87 


.97 


1.03 






.952 


15 


.90 


1.01 


1.03 


1.05 






.958 


16 


.92 




.94- 


1.04 


0.94 


1.10 


.953 


17 


.89 


.95 


.91 


.99 


.99 




.932 


18 


.89 


.98 


.90 


.96 


1.13 


1.00 


.934 


19 


.96 


.90 


.94 


.98 


.99 




.954 


20 


1.05 


.95 


.88 


.97 


.94 


.99 


.937 


21 


.90 




.88 




.94 


.92 


.902 


22 




.92 


.89 


.94 


.96 


.99 


.938 


23 


.93 


.97 


.94 


.88 


1.00 


.91 


.926 


24 


.93 


.94 


.87 


.95 






.921 


25 




.96 


.94 


.98 


1.04 




1.000 


26 


.94 






.90 


1.07 


.90 


.934 


27 


.93 




.96 


.95 


.93 


.95 


.941 


28 








.93 


.80 


.101 


.913 


29 






1.01 


.93 






.970 


30 






.98 


.85 


.96 




.948 


31 


.94 


.80 


.84 




1.13 




.927 


32 






.94 




.89 




.915 


33 
















34 




.92 




.85 


.80 




.817 


Av'g'd by height, 














Weighted 


weighted 


0.939 


0.961 


0.932 


0.958 


0.966 


0.962 


average 0.9468 



It is possible, of course, to prepare a table of frustum volumes using 
fixed top diameters, and compute the form factors of trees for those 
classes whose top diameters are larger or smaller, but in this case the 



CALCULATION OF THE VOLUMES OF FRUSTUMS 



223 



form factors vary not with form alone but also with difference in volume 
due to difference in top diameter independent of form. The results 
are shown in Table XXXVI where an average top of 13.2 inches was 
used on all frustums. 

TABLE XXXVI 

Frustum Form Factors for 555 Longleaf Pines, Coosa County, Alabama, 
Based on Average Top Diameter of 13.2 Inches for Frustums 





Merchantable Length in 


16-foot Logs 








2 


2h 


3 


3§ 


4 


^ 


D.B.H 














Inches 


Frustum Form Factors 


14 


0.53 


0.53 


0.54 








15 


.57 


.59 


.50 


.55 






16 


.71 




.51 


.56 


0.53 


0.57 


17 


.67 


.76 


.65 


.69 


.60 




18 


.88 


.55 


.72 


.74 


.77 


.69 


19 


1.03 


.81 


.84 


.81 


.78 




20 


1.13 


1.00 


.87 


.96 


.87 


.86 


21 


1.31 




.98 




.85 


.79 


22 




1.39 


1.00 


.99 


1.01 


.88 


23 


1.54 


1.39 


1.19 


.98 


1.09 




24 


1.40 


1.40 


1.13 


1.26 






25 




1.37 


1.34 


1.33 


1.06 




26 


2.60 


.95 


1.85 


1.21 


1 47 


.97 


27 


1.97 




1.52 


1.22 


1.23 


1.14 


28 








1.26 


.97 


1.27 


29 






1.67 


1.35 






30 






1.98 


1 37 


1.17 




31 


2.36 


1.04 


1 18 


1.68 


1.51 




32 






1.76 


.... 


1.43 





Such a table serves no useful purpose. 

The variation of top diameters actually utilized is shown in Table 
XXXVII. 

The values in this table, evened off by curves, would give proper 
dimensions for frustums for the volume table desired. 

The two steps described mean a double calculation of frustum 
volumes, first, as a basis of regular form factors, second as a basis of 
regular volumes. The second set of frustums also serves the purpose 
of obtaining the volumes for exact diameter and height classes, instead 
of for the actual average diameters and heights of the trees measured 
(§ 137). 



224 



FRUSTUM FORM FACTORS 



TABLE XXXVII 

Actual Average Top Diameters of Merchantable Lengths, Longleaf Pine, 
Coosa Co., Ala. Basis 555 Trees; Average of All Top Diameters 13.2 
Inches 

Merchantable Length in 16-foot Logs 



D.B.H. 


2 


2^ 


3 


31 


' 


4^ 


5 


Inches 




Top Diameters, Inside 


Bark — Inches 




10 
















11 
















12 


9.5 


8.5 












13 


9.7 


7.5 


8.8 










14 


9.9 


9.2 


9.3 


8.7 








15 


10.4 


10.3 


8.9 


9.1 








16 


11.5 




10.4 


9.3 


8.6 


7.8 




17 


11.3 


11.5 


10.4 


10.2 


9.1 






18 


13 1 


12.7 


11.5 


10.7 


9.7 


9.6 




19 


13.8 


12.3 


12.1 


11.3 


10.9 


9.2 




20 


13.7 


13.5 


13.1 


13.1 


12.3 


11.6 




21 


16.7 




14.1 


13.2 


12.1 


11.4 




22 




17.4 


14.2 


13.7 


13.5 


11.7 


11.0 


23 


18.0 


17.0 


15.8 


14.2 


14.1 


13.8 




24 


17.4 


17.7 


16.2 


15.9 


14.1 






25 




17.2 


17.5 


16.7 


13.3 






26 


21.3 


15.4 


19.7 


16.9 


17.7 


14 1 




27 


21.6 




19.4 


16.3 


17.1 


16.0 




28 








17.4 


16.2 


16.6 




29 






20.5 


18.8 








30 






24.0 


20.8 


16.2 




17.3 


31 


25.3 


16.4 


18.3 


14.6 


17.8 






32 






23.2 




21.2 






33 
















34 




26.8 




21.0 


22.4 







Of the two methods, the use of a fixed top diameter is preferable 
wherever utiHzation does not depart too far from this standard. If 
necessary, such a table of volumes could be corrected for actual utili- 
zation, by subtracting the per cent of volume lost by cutting to a lower 
point and larger diameter. In this case the same method must be used 
in estimating the standing timber, namely, to tally the heights of the 
trees to the fixed top diameter used, and then discount for waste. 

185. Construction of the Volume Table from Frustum Form Factors. 
A Short Method. The third and final step is to construct the volume 
table by multiplying the volumes of the frustums by the form factors 
for each class, 



FORM FACTORS FOR BOARD FEET 225 

Frustum form factors can be computed if desired, in cubic feet. 
For board feet, any log rule may be used as desired. 

A shorter but less satisfactory method is to first determine the top 
diameters of the frustums to be used in the base table and prepare the 
table of frustum volumes; second, to compute the arbitrary form 
factors which are obtained by dividing the average volumes of the trees 
in each class by the volume of the proper frustum, disregarding the 
possible difference in top diameter and average height for the class; 
and from these factors, to construct the volume table. This method 
works best when fixed top diameters are used in logging and the dif- 
ferences in top diameters between frustums and trees is small. 

The method of frustum form factors has resulted in such a marked 
increase in accuracy and economy in preparation of standard volume 
tables based on merchantable board-foot contents that it has practically 
superseded the standard methods of preparing these volume tables, 
and until total height and tables based on form classes supersede the 
use of mercha-ntable heights in timber estimating, this method will 
continue to be used extensively. 

186. Other Merchantable Form Factors for Board Feet. Merchant- 
able form factors based on the volume of a cylinder whose height equals 
the merchantable length in the tree have been proposed by E. I. Terry. 

Merchantable volume tables based on the contents of frustums of 
paraboloids whose top diameters equal one-half D.B.H., scaled in 16- 
foot logs, have been computed by the Forest Service. These correspond 
in principle to the basic volumes of frustums of cones, and can be used 
for calculating form factors in the same manner, but offer no special 
advantage over the frustums of cones for the purpose required. 

References 

A New Method of Constructing Volume Tables, Donald Bruce, Forestry Quarterly, 

Vol. X, 1912, p. 21.5. 
The Use of Frustum Form Factors in Constructing Volume Tables, Donald Bruce, 

Proc. Soc. Am. Foresters, Vol. VIII, 1913, p. 278. 
Further Notes on Frustum Form Factor Volume Tables, Donald Bruce, Proc. Soc. 

Am. Foresters, Vol. X, 1915, p. 315. 
The Use of Frustum Form Factors in Constructing Volume Tables for Western 

Yellow Pine in the Southwest, Clarence F. Korstian, Proc. Soc. Am. Foresters, 

Vol. X, 1915, p. 301. 
Top Diameters as Affecting the Frustum Form Factor for Longleaf Pine, H. H. 

Chapman, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 185. 
Frustum Form Factors of Hard Maple and Yellow Birch, B. A. Chandler, Bui. 210, 

Vermont Agr. Exp. Sta., May, 1918. 
A Formula Method for Estimating Timber, E. I. Terry, Journal of Forestry, 

Vol. XVII, 1919, p. 413. 
Comment on Above, Donald Bruce, Journal, Vol. XVII, 1919, p. 691. 
Further Comment, E. I. Terry, Journal, Vol. XVIII, 1920, p. 160, 



CHAPTER XVIII 
THE MEASUREMENT OF STANDING TREES 

187. The Problem of Measuring Standing Timber for Volume. 

Standing trees are measured to determine their contents in cubic feet 
or in terms of manufactured products such as board feet or cross-ties. 
Trees are measured as a means of determining the contents of entire 
stands. These may be either average or sample trees, of which only 
a few are measured, or all of the trees in a stand or part of a stand may 
be tallied. 

The volumes contained in standing trees cannot be measured directly. 
Even the volume of the logs in the felled tree is computed from the 
measurement of their diameters and lengths. These computations, 
tabulated as log rules and as volume tables reduce the problem of esti- 
mating the volume of standing trees to that of measuring their merchant- 
able lengths and diameters. 

The cruiser must determine the height of trees either by instruments 
based on geometric principles of similar triangles, at considerable 
expenditure of time or by the eye, which is the only practical method 
where all or a large portion of the stand is to be so measured. 

Still more difficult is the actual measurement of diameters at the 
top of each log in the standing tree, which must be known when log 
rules are substituted for volume tables in timber estimating. Instead, 
the cruiser measures the diameter within reach, that at B.H. or stump, 
and judges the rate of taper as well as height, by eye, thus arriving at 
these upper diameters by calculation from a known measurement. 

Diameter breast high (D.B.H) is the only actual and accurate 
measurement which it is practicable to take upon all or a large per cent 
of the timber. All upper points are either measured on a few trees 
only, to obtain averages, or else are judged solely by eye; and since 
such ocular measurements are confined to dimensions, heights or log 
lengths, and diameters at upper points on the bole, the cruiser is depend- 
ent entirely on the computed volumes for these dimensions shown in 
log rules or volume tables. He may by experience correlate these 
volumes with their respective dimensions, just as stock buyers learn 
to guess the weights of animals, and may arrive directly at the volume 

226 



THE MEASUREMENT OF TREE DIAMETERS 227 

of the tree or stand, but the method is far more uncertain than if depend- 
ence is placed on the computed vohimes of the logs or trees as shown 
in tables. 

In the use of volume tables, then, the accepted standards of volumes 
set by these tables are substituted for guessing as to the contents. 
The measurements required may be : 

1. Diameter at base. 

a. Standardized at D.B.H., outside bark. 
h. Stump diameter inside bark, still in use by old time 
cruisers. 

2. Height of tree. 

a. Total height to tip. 
h. Merchantable height. 

1'. To a fixed top diameter. 

2'. To a variable top diameter. 

3. Actual measurement of an upper diameter to determine 

form (when form classes are distinguished). 

a. At middle of stem above D.B.H. (Jonson). 
h. At middle of stem above stump (Schiffel). 
c. At top of last log. 

188. The Measurement of Tree Diameters — Diameter Classes. 
Stand Tables. Diameters will be averaged in either 1-inch or 2-inch 
classes. In the East and with species of a small total range of diameters, 
1-inch classes are preferable. Especially with such species as spruce 
and white pine, 1-inch diameter classes are necessary to give a proper 
basis for determination of the rate of growth, and the number of such 
classes is not great enough to act as a drawback in estimating. 

A stand table is a tabular statement of the number of trees, in 
each diameter class standing on a given area. By dividing the total 
stand table by the area in acres, the stand per acre is shown, in which 
case the trees in each diameter class are usually expressed in decimals 
to two places, e.g., 12-inch class, 4.63 trees, etc. 

On the Pacific Coast, with a wide range of diameters running up 
to 60 inches or over, it is unnecessary and inadvisable to make smaller 
than 2-inch diameter classes.^ 

189. Instruments for Measuring Diameter. Calipers, Description 
and Method of Use. Calipers have been the standard instrument 

1 In French forest practice, 5 centimeters is the division used. This corresponds 
to 1.97 inches. 

The centimeter divisions were evidently too small and the next convenient 
division point was 5 centimeters. This is not an argument against the use of 
1-inch diameter classes for Eastern species. 



228 



THE MEASUREMENT OF STANDING TREES 



for measuring the diameter of standing trees and their use is necessary 
in taking taper measurements on down timber which cannot be meas- 
ured with diameter tape. The standard type of cahpers for eastern 



n 



--. [\ 



i»ipif}f«ig««5 



kjjIJIiB^^ 



Fig. .39. — Calipers used in measuring the diameters of standing trees. 

hardwoods has a beam 36 inches long with arms one-half that length. 
A smaller type may be used for trees whose diameter does not exceed 
2 feet as in spruce or second-growth timber. The standard calipers 
have a beam graduated on both sides to inches and tenths, and two 
arms, one of which is bolted to the end of the beam, the other a sliding 

arm, the beam 
passing through a 
slot. 

Fig. 40 indicates 
the construction 
of this arm. The 
essential feature 
is that when not 
pressed against 
the tree, the arm 
-Construction of calipers, to secure adjustment of jg easily moved 




Fig. 40. 

movable arm at right angles to bar. along the beam 

but when in use 
it takes a position at right angles with the beam and parallel to the 
other arm. The position of this arm is adjustable by the movement of 
the screw (a) which sets a movable plate. 

In use the arms must be at right angles to the beam. If warped or 
out of adjustment, corresponding errors in measuring diameters will 
occur. The correct diameter can be obtained only by holding the cali- 



THE DIAMETER TAPE 



229 



pers horizontally, with the beam in contact with the tree at the point 
desired, usually at B.H. If measured with the tips of the calipers, 
the errors resulting from false adjustment or warping are exaggerated. 
If measured with the calipers held at an angle, the point measured is 
probably above D.B.H. and correspondingly too small. If measured 
below D.B.H., a large error results from the rapidly increasing diameter 
of the tree due to stump taper. An average measurement 6 inches 
below the desired point or at 4 feet will incur from 5 to 8 per cent excess 
volume, depending upon the rapidity of the taper. 

Where the exact average diameter of a tree is desired, two measure- 
ments must be taken at right angles and the mean recorded to to inch. 
In timber estimating, where large numbers of trees are measured, but 
one diameter is taken, with no efforts made to determine the average 
even on trees of eccentric cross sections since it is assumed that errors 
incurred in this way are compensating. A precaution sometimes used 
is to measure half of the trees in one cardinal du'ection, and the remainder 
in the other (French). 

190. The Diameter Tape. The irregularity in the form of trees, 
both as to cross section and bark, makes it practically impossible to 
obtain consistent results in two successive measurements of diameter 
of the same tree 
with calipers even 
when the mean 
diameter is taken 
as above indicated. 
For permanent 
records on plots 
to be subsequently 
measured for deter- 
mination of growth, 
consistency in 
diameter measure- 
ment is absolutely 
required. 

For this purpose it has been found that the diameter tape must be 
substituted for calipers. The graduations on the diameter tape are in 
inches of diameter, each inch equal to 3.1416 inches in girth. In theory, 
the measurement of the circumference of a tree gives a plus error when 
compared with the actual mean diameter. Actual tests at the Fort 
Valley Experiment Station by Scherer on one hundred trees showed 
that the excess in diameter from tape over caliper measurement was 
2 per cent, but the consistency of two successive tape measurements 
as compared with successive caliper measiu-ements showed that the 




Fig. 41. — Tape for measuring girths and diameters. 



230 



THE MEASUREMENT OF STANDING TREES 



total error of calipers over tape was in the proportion of 21 to 1. The 
diameter tape should therefore be adopted for all measurements of 
permanent sample plots. 

191. The Biltmore Stick. Although calipers can be taken apart 
for travel and packing, they are cumbersome to carry in timber esti- 
mating especially through brush and over rough ground. When in 
addition a beam of 60 inches in length is required, their use becomes 
extremely burdensome. 

The Biltmore Stick, devised by Dr. C. A. Schenck, substitutes a 
straight stick for calipers and has been widely adopted by foresters 
for practical timber cruising. 

The principle of the Biltmore Stick is as follows : A straight stick, 
if held horizontally, tangent to or in contact with the bole of the tree, 
and at arm's length from the eye, forms the far side of a triangle whose 
other two sides are lines of sight from eye to each side of the tree, and 
which intersect the stick at definite points. When the stick is held 

so that one of 
these lines of 
sight intersects 
one end, a scale 
can be placed 
upon the stick 
starting at zero 
at this end, and 
the point of in- 
tersection of the 
other line of 
sight, if the eye 
is held in its original position without turning the head, will indicate 
on the scale the diameter of the tree at this point. 

Since this intercepted distance on the stick is evidently less than the diameter 
of the tree, which is at a greater distance and cannot even be seen correctly, the 
distances corresponding to the diameters wanted will be less than these diameters 
and this difference increases with diameter of tree, so that the graduations on the 
stick for successive diameters fall closer together for the larger diameters. The 
values of the graduations on the stick are directly dependent on the dimensions 
of the triangle which is determined by the length of the arm or reach. This ranges 
from 23 to 27 inches with an average of 25 inches. 




Fig. 42. 



-Principle upon which the Biltmore stick is 
constructed. 



The formula for computing the values of this scale is 
a = length of reach in inches; 
D = D.B.H. 



THE BILTMORE STICK 231 

Scale = 



Va{a+D) 






'a+D 
The derivation of this formula is as follows : 









AB 


AB' 








BC 


B'C 






AB = 


= a inches, 


an( 


Substituting 


these va 


lues, 
a 
BC' 


AB' 
D ' 
2 








aU 
2 


= AB'XBC. 


(I) 




SC- 


aD 

2 

AB" 





D 
2' 



{AB'Y = {AC'Y-{B'C')\ 
By substitution, 

{AB'y=la+-\ -(-) ={ay+aD = a{a-\-D). 



2/ \ 2j 
(II) AB' = yya{a+D). 

Substituting this value for AB' in equation (1), 

aD 
BC. ^ 



Vaia+D)' 

Since BC is the scale for ^ of the diameter of the circle, the formula for the scale 
for the whole circle is ^ 



„ , aD laD'^ 

Scale =- 



~\^+D 



Vaia+D) yla+D' 

The Biltmore stick is less accurate than the caHpers or diameter 
tape and should therefore never be used for scientific measurements or 
permanent records. To insure complete accuracy in the use of a prop- 
erly graduated stick, the following conditions are necessary: 

The tree must be circular in cross-section. 

The stick must be held against the tree at a point 4| feet from the 
ground. 

aD VaVaD VaD foD^ 



VaVaD VaD ja^ 

VaVa+D Va^ >«" 



Vaia+D) VaVa+D Va+D \a+£> 



282 



THE MEASUREMENT OF STANDING TREES 



The eye must be on a level with the stick (assuming that the tree 
is erect). 

The eye must be at the proper distance from the tree. 

The stick must be held horizontal (assuming again that the tree 
is erect). 

The stick must be held perpendicular to the line of sight from the 
eye to the center of the tree at the point of measurement. 

Errors of 1 per cent in the measurement of diameter are incurred 
under the following conditions : 

The figures given represent the distances by which the position 
of stick or eye departs from the above conditions. 

TABLE XXXVIII 
Errors in Using Biltmore Stick * 



Sign 




Resulting in Error of 
1 Per Cent in Diameter 



D.B.H. of trees 



10 


30 


Inches 


Inches 


9.2 


7.3 


4.6 


4.2 


4.9 


4.9 


1.4 


0.65 



60 

Inches 



+ 



+ 



± 
Usually 



Eye above or below stick by 

Stick not horizontal — one end higher than 

other by 

Stick not perpendicular to hnc of sight — one 

end nearer the eye than the other by 

Eye too near to or too far from tree by 

Measurement at wrong height 

Tree irregular in shape 



7.1 

4.1 

5.1 
0.45 



(Variable) 

(Very variable — consider- 
ably greater than with 
calipers) 



* Donald Bruce, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 46. 

A still more serious error is incurred through the inevitable tendency of the 
cruiser to raise the stick to the level of the eye, rather than lower the eye to the 
level of the stick. If the stick is held at 4^ feet and the eye remains at 5 feet 
3 inches, with a difference of 7 inches in height, the error is but 1 per cent of the 
diameter, but if the stick is raised to the level of the eye, the diameter at the point 
measured is appreciably less than D.B.H. The resultant average error varies from 
3 to 6 per cent, dependent upon the rapidity of taper, and increases consequently with 
the diameter of the tree. 

The following table gives the graduations which should be placed upon Biltmore 
sticks for a reach of from 23 to 27 inches respectively: 



THE BILTMORE STICK 



233 



TABLE XXXIX 

Figures to be Used in Graduating a Biltmore Stick * 





Distance from Eye to Tree — Incites 


Diameter 












of 


23 


24 


25 


26 


27 


tree. 












Inches 


Distance to be marked on stick — Inches 


3 


2.82 


2.83 


2.83 


2.84 


2.85 


5 


4.53 


4.55 


4.56 


4.58 


4.59 


7 


6.13 


6.16 


6.19 


6.21 


6.24 


9 


7.63 


7.68 


7.72 


7.76 


7.79 


11 


9.05 


9.11 


9.17 


9.22 


9.27 


13 


10.39 


10.47 


10.54 


10.61 


■ 10.68 


15 


11.67 


11.77 


11.86 


11.94 


12.03 


17 


12.89 


13.01 


13 . 12 


13.22 


13.32 


19 


14.06 


14.19 


14.32 


14.44 


14.56 


21 


15.18 


15.34 


15.48 


15.62 


15.75 


23 


16.26 


16.44 


16.60 


16.75 


16.90 


25 


17.31 


17.50 


17.68 


17.85 


18.01 


27 


18.31 


18.52 


18.72 


18.91 


19.09 


29 


19.29 


19.51 


19.73 


19.94 


20.14 


31 


20.23 


20.48 


20.71 


20.94 


21.15 


33 


21.15 


21.41 


21.67 


21.91 


22.14 


35 


22.04 


22.32 


22.59 


22.85 


23.10 


37 


22.91 


23.21 


23.50 


23.77 


24.03 


39 


23.75 


24.07 


24.37 


24.67 


24.94 


41 


24.58 


24.91 


25.23 


25.54 


25.84 


43 


25.38 • 


25.74 


26.07 


26.40 


26.71 


45 


26.17 


26.54 


26.89 


27.23 


27.56 


47 


26.94 


27.33 


27.70 


28.05 


28.39 


49 


27.69 


28.10 


28.48 


28.85 


29.21 


51 


28.43 


28.85 


29.25 


29.64 


30.01 


53 


29.16 


29.59 


30.01 


30.41 


30.79 


55 


29.87 


30.31 


30.75 


31.16 


31.56 


57 


30.56 


31.03 


31.47 


31.90 


32.32 


59 


31.25 


31.73 


32.19 


32.63 


33.06 


61 


31.92 


32.41 


32.89 


33.35 


33.79 


63 


32.58 


33.09 


33.58 


34.05 


34.51 


65 


33.23 


33.75 


34.26 


34.74 


35.21 



*W. B. Barrows, Journal of Forestry, Vol. XVI, 1918, p. 747 

In this table, the graduations are given for odd diameters instead of even ones. 
For instance, when diameters are taUied in 2-inch classes, every tree larger than 
13 inches and smaller than 15 inches in diameter is tallied as a 14-inch tree. 
These graduations thus mark the upper and lower limits of size of each 2-inch 



234 THE MEASUREMENT OF STANDING TREES 

D.B.H. class, instead of the average size, as 14 inches, enabhng the cruiser to 
classify accurately all trees on the border line between two diameter classes. 

In measuring trees of eccentric or irregular cross section, the errors incident to 
caliper measurement are exaggerated by the use of the Biltmore stick, but as before, 
these errors tend to compensate and can be neglected. 

Bruce has suggested that the volume tables standardized at D.B.H. should be 
converted to values for diameter at the height of the eye, or D.E.H., standardized 
at 5 feet 3 inches. To do this, taper measurements are taken to establish the 
D.E.H. of trees of given D.B.H. By interpolation, the volumes corresponding to 
given even D.E.H. inches can easily be obtained. 

In the ordinary use of the Biltmore stick, it is necessary to bevel the edge 
opposite the figures so that the measurement may be taken in contact with the bole. 
Otherwise the thickness of the stick reduces the distance from the eye and incurs 
an error whose magnitude is determined by this thickness. By deducting this 
thickness (t) from the distance (a) in the formula, so that this formula reads, 

Scale = 



Va{a+D) 
the resulting values are correct for the face of the stick. 

192. Ocular Estimation of Tree Dimensions. Where the diameter 
of every tree on a given area must be recorded, the time consumed in 
actually measuring the diameters is a considerable item of expense. 
Except when scientific measurements or permanent plot records are 
required, estimators plan to educate the eye to read as large a percent- 
age as possible of the diameters directly without measurement, using 
the calipers, diameter tape or Biltmore stick merely as a check. This 
is especially desirable when the cruiser is doing his own tallying. 

While the eye can be trained with considerable rapidity to a sufficient 
degree of accuracy for estimating, it is constantly liable to error and 
must never be relied upon for even a single day without instrumental 
checks. These should be made on starting work and at intervals during 
the day. The eye may be trained to judge diameters at different 
distances equally well. Some men develop this faculty more rapidly 
and to greater degree than others. It is the general tendency in ocular 
estimation to favor a tree of a given size, diameters of trees of lesser 
size being over-estimated while larger diameters are under-estimated. 
The use of 2-inch diameter classes greatly facilitates ocular estimating. 

In training the eye to estimate diameters, the greatest progress is 
made by repeated guesses followed immediately by the measurement 
of the tree which is then closely observed to fix the known diameter and 
correct the faulty observation. Since ocular estimating is not a matter 
of reasoning but of impression, the decision as to the dimensions of the 
tree should be made instantly. Otherwise fatigue and consequent 
inaccuracy ensue. 



THE MEASUREMENT OF HEIGHTS 235 

193. The Measurement of Heights. While in measuring diameters 
it is possible to use the instrument upon every tree as a practical measure 
when necessary, the greater difficulty and time required in measuring 
heights makes the general use of an instrument for even a large per 
cent of the trees impossible. Only on small, permanent sample plots 
will the height of each tree be actually measured. Height measures, 
or so-called hypsometers, are commonly used to obtain the height 
of average trees from which the average height of the remaining trees 
is determined, or to check the eye when the merchantable heights of 
all trees are recorded. 

In the latter case, ocular estimation of the number of merchantable 
logs in each tree, or total merchantable height, is the only practical 
means possible. It takes no longer to estimate the height of a tree 
by eye than its diameter, but the measurement of height by hypsometer 
takes about ten times as long as to caliper the tree. 

The eye is slightly more unreliable in measuring heights than diam- 
eters. The height scale is more difficult to fix in the mind. Con- 
sequently the tendency is to arrive at the height of trees by comparison 
with other trees. The result is that the standard of height for all trees 
tends to shift from day to day unless heights are carefully checked at 
the beginning of each day's work in order to maintain this mental 
basis or standard. In no other feature of ocular timber estimating 
are such serious errors made even by experienced cruisers as in estimat- 
ing heights, and the novice should never trust his judgment over- 
night. 

194. Methods Based on the Similarity of Isoceles Triangles. 
Measurement of heights is based on the principles of similar triangles. 
From the observer's eye, the tree forms one side of a large triangle, 
the other two sides of which are the lines of sight to the top and base 
of the tree. The base of this triangle can be measured. The length 
of the vertical side which is the height of the tree is the dimension 
sought. To determine this inaccessible dimension, a smaller, measure- 
able, similar triangle is used. 

Similar triangles must have their three sides proportional and the 
three angles equal. This is secured when either two sides are propor- 
tional and one angle equal, or one side is proportional and two angles 
equal. 

The isosceles triangle with two sides of equal length forms the 
simplest method of measuring the height of a standing tree. In this 
triangle the base from the eye to the foot of the tree is equal to the 
height of the tree and may be directly measured. The small triangle 
in this case is used to find the point on the ground at which this base 
will be equal to tree height. A triangle which has its own base and 



236 



THE MEASUREMENT OF STANDING TREES 



/ 



y 



hy 



X 



height equal and whose Hne of sight from eye to top coincides with that 
from eye to tip of tree gives this result. 

A straight stick or short pole may be grasped by the thumb and first 
finger at a distance from its top exactly equal to the distance from the 
eye to the point thus marked. Holding this stick vertically, which 
is best accomplished by having the greatest weight below the hand 
to act as a pendulum, the observer moves backward or forward until 
the line of sight ^6 in Fig. 43 cuts the desired upper point on the tree, 
and at the same time the line of sight '.Ac cuts the tree at its base. At 
this point the triangle Ahc has become similar to the triangle ABC, 
and AC is equal to BC. The measured distance from eye to base of 

tree is then equal to the 
height of the tree. This 
distance can be measured 
along the ground to the 
point below the eye with 
sufficient accuracy, pro- 
vided the slope is even. 
Thismeasurementof height 
can be taken from any 
point of elevation, either 
on a level with, above, 
or below the base of the 
tree without affecting its 
accuracy. 

195. The Principle of 
the Klaussner Hypsom- 
eter. For height meas- 
urements which require 
greater accuracy than is obtainable by such ocular methods as the 
one just described, the small triangle is constructed in the form 
of an instrument called a hypsometer, on which two of the sides 
corresponding respectively to the lines AC and BC, or distance 
to tree and height of tree, are graduated to units of distance. This 
enables the observer to first adjust the scale AC for distance, 
to equal in feet the known distance from the tree, hence to determine 
what this distance shall be. The line of sight from the eye, beginning 
at the zero point of this scale or apex of the small triangle is now brought 
into line with the point on the tree whose height is to be measured, 
which makes the small and large triangles similar. The point at which 
this line of sight cuts the scale BC, whose graduations are equal to those 
on the scale AC indicates the height of the tree. These graduations 
may be of any size so long as both scales are graduated equally. They 




;.i^Jc 



Fig. 



43. — Similar isosceles triangles formed by use 
of pole, for measuring height of trees. 



THE PRINCIPLE OF THE KLAUSSNER HYPSOMETER 



237 



will serve to read height in feet, or in any other unit of distance, as 
meters, since whatever unit is used 
to measure the distance from the 
tree applies as well to its height. 

The Klaussner Hypsonieter. In 
hypsometers based upon similar 
triangles as shown in Fig. 43 the 
vertical scale represents tree height, 
the scale at base, distance to the 
tree. If the scale fee is on a movable 
arm, it may be set on the scale Ac 
at any required distance. By sight- 
ing along Ac towards C and by rais- 
ing the sight or bar Ah to intersect 
the line of sight AB, the total 
height of tree is read directly from 
the scale fee. The standard hyp- 
sonieter of this make is known as 
the Klaussner, Fig. 44. The verti- 
cal scale is weighted to insure its 
vertical position. 

As is seen, two lines of sight 
must be adjusted for this reading. The instrument is therefore used 
with a tripod and is rather slow in execution.^ 




Fig. 44. — The Klaussner hypsometer. 




"^f^ 




L 



Fig. 44o. — Method of application of the Klaussner hypsometer. 



-■'-ni,''~ . 



> In Forestry Quarterly, Vol. XHI, 1915, p. 442, S. B. Detwiler has suggested a 
simple hypsometer based upon this principle, which for practical work does away 
with the tripod apparently without sacrificing accuracy. 



238 THE MEASUREMENT OF STANDING TREES 

The Klaussner principle differs from that shown in Fig. 43 only 
in that the height is measured on the vertical scale be, the measure- 
ment may be taken at any point from the tree by adjusting the scale 
Ac to correspond with this distance, and the triangles may be of any 
form, provided one side is vertical. 

Merritt Hypsometer. The Merritt hypsometer is a scale placed on 
the reverse side of the Biltmore stick (§ 191) and is read by holding the 
stick in a vertical position at arm's length, when standing at a given dis- 
tance from the tree. 

Six inches on the stick will give the height of a 16.3-foot log under 
the following conditions: 

Arm length, inches 23 24 25 26 27 

Distance from eye to tree, feet 62 , 5 65 . 2 67 . 9 70 . 6 73 . 3 

The similar triangles used here correspond in principle with those 
of the Klaussner hypsometer. 

For accurate results the stick must be held vertically and not raised 
or lowered during the reading. Only approximate accuracy can be 
secured, but the method serves as a ready check on ocular measure- 
ments of log lengths. 

196. Methods Based on the Similarity of Right Triangles. The 
second general method for measuring heights is the use of the right 
triangle. This method is based on securing a horizontal line of sight 
from the eye to a point on the bole of the tree, and requires two 
readings, one above, the other below this point of intersection, the sum 
of which gives the height of the tree. This disadvantage is offset by the 
fact that these instruments may be held in the hand, thus eliminating 
the tripod, and making them compact and portable. 

The horizontal line of sight may be secured by using either a bubble 
or a plumb-bob. The simplest application of this method is that of a 
right isosceles triangle, for which purpose a clinometer is used. This 
is an instrument with bubble mounted on a graduated arc reading in 
per cents, or in degrees. In the latter case the graduations must be 
reduced to per cents. 

When the arc on this clinometer is set at an angle of 45°, the line 
of sight Ab coincides with the line AB at a, definite distance from the 
tree, from which a horizontal line of sight, which can then be taken by 
setting the arc at zero, gives a distance to the tree equal to the height 
of the tree above the intersection of this line with the bole. If used 
on fairly level ground, the distance below this point is within reach and 
can be measured on the tree and added to the distance to the tree to 
get its total height. 

This instrument can also be used to measure heights from any dis- 
tance from the bole, by taking two readings or angles, one to the upper 



HYPSOMETERS BASED ON PENDULUM OR PLUMB-BOB 239 

point, and one to the base. In this case the actual angle from station 
to point on tree is read, and indicates the height in per cent of the hori- 
zontal distance. At 100 feet distance, an 80 per cent angle to tip 
equals a height of 80 feet above the eye. If the lower angle to base is 




Fig. 45. — The Abney hand level and clinometer. 

now 5 per cent, the additional height is 5 feet, total height 85 feet. 
At 50-foot distance these per cents applied to 50 feet give a total height 
of 42| feet. It is convenient therefore to read heights by this method 
from distances easily converted into equivalent heights. 




Fig. 46. — Goulier's Clinometer. 



197. Hypsometers Based on the Pendulum or Plumb-bob. These 
angles can be read as easily from a pendulum, with graduated arc placed 
below. A clinometer constructed on this principle, and used as a 
hypsometer, is illustrated in Fig. 46. 



240 



THE MEASUREMENT OF STANDING TREES 



The Fauslmann Hypsometer. Instead of graduating a circular arc 
in per cents, which requires a decreasing scale with increasing per cent 
(since the tangents of the angles increase faster than the angle), the 
height scale corresponding with this arc may be placed on a straight 
arm as in other hypsometers (§ 195) and graduated evenly. 

The Faustmann hypsometer employs this principle of the pendulum, 
using a plumb-bob to determine the angles BAD and CAD, and indicat- 
ing the height of the tree above and below the point D by the intersec- 
tion of this plumb-bob string with the " height "scale on the base of the 
hypsometer. This instrument is illustrated in Fig. 47. Its method 
of use is shown in Fig. 48. 




Fig. 47. — The Faustmann hypsometer. 

The slide is first moved upwards until the number of units on the 
vertical scale, from zero, thus set off, equals the distance to the tree 
in feet (or in yards). When sighted at the upper point on the tree, 
the plumb-bob falls to the near side towards the eye, and the number of 
units or height is read in the mirror. The second reading is shown in 
Fig. 48, the plumb-bob falling to the far side. The horizontal scale thus 
extends in both directions from zero. On fairly level ground, this 
second reading is sometimes omitted, providing the height of the eye 
above the base of tree is regarded as a constant and added for total 
height. For accurate measurements both readings must be taken. 

Practice has demonstrated that the use of a plumb-bob and weight 
reduces the serviceable character of the instrument, since the seweights 
are easily lost and the strings broken. The mirrors also are easily 
damaged. 

Weise Hypsometer. The Weise hypsometer (Fig. 49) is the same 
in principle as the Faustmann but substitutes a metal pendulum for 



HYPSOMETERS BASED ON PENDULUM OR PLUMB-BOB 241 



the string and plumb-bob. The two arms when not in use can be placed 
within the cylinder. The instrument is more durable than the Faust- 
mann but slightly less accurate. 

Forest Service Hypsometer. A more durable type of hypsometer 
based upon this principle is known as the Forest Service hypsometer. 
The distance at which this instrument reads the heights BD and DC 
is fixed at 100 feet. The scale showing these heights is computed from 
the tangents of the angles read at this distance and expressed in terms 
of feet in height. This scale is placed on a circular pendulum which 







Fig. 48. — Method of application of the Faustmann hypsometer. 



is released by pressing a small knob with the thumb while sighting 
through a peep-hole along the line of sight AB or AC. This scale is 
enclosed in a metal frame in the form of a disk, and the instrument is 
practically indestructible and can be operated with one hand. If read 
at 50 feet, the readings shown must be divided by two. If at 200 feet, 
they must be multiplied by two, and proportionately for other distances. 
As in the case of other clinometers this hypsometer may be used to read 
per cents of grade. 

The Winkler Hypsometer. The same principle may be used in 
constructing a hypsometer in the form of a square or rectangular 
board or cardboard. In this instrument the line of sight, AB, coin- 
cides with the top edge of the board. 

A board whose top and bottom edges are parallel is laid off with a 



242 



THE MEASUREMENT OF STANDING TREES 



horizontal scale at base and a vertical scale ad intersecting the scale 
at base at right angles, at a point to permit this horizontal scale to extend 
in both directions as in the Faustmann Hypsometer. Both scales are 
marked off in the number of equal units or graduations desired, to cor- 
respond with the distance from the tree at which the hypsometer is to 
be used. A plumb-bob is suspended from point a, and the heights above 
and below the eye read as usual. If but one fixed distance is desired 
this is represented by a scale reproduced on the line at base of card. 




Fig. 49. — The Weise hypsometer. 



This board may be graduated to read at lesser distances from the 
tree, by placing other horizontal scales upon the board intersecting 
the vertical or " distance " scale ad at the point below the apex a, 
representing the distances desired, and graduating these horizontal 
lines to the same scale as the base. This home-made hypsometer is 
described in Farmers' Bulletin 715, U. S. Dept. of Agriculture, 1916, 
p. 18. 

The original instrument from which this type of hypsometer was 
derived is known as the Winkler hypsometer, shown in Fig. 50. This 
instrument is also used as a dendrometer (§ 200). 



THE PRINCIPLE OF THE CHRISTEN HYPSOMETER 



243 



198. The Principle of the Christen Hypsometer. Many hypsom- 
eters have been invented, principally by Continental foresters, using 
one or the other of these general principles. The Christen hypsometer 
introduces a different principle but has no special merit except the 
simplicity of its operation. Description of this instrument, taken 
from Graves' Mensuration is as follows : 

This instrument consists of a metal strip 16 inches long, of the shape shown in 
Fig. 51. The instrument is made of two pieces hinged together, which are folded 




Fig. 50. — Winkler Hypsometer. 

when it is not in use. A hole is pierced in the upper end, from which it is suspended 
between the fingers. Along the inner edge is a notched scale which gives directly the 
readings for heights. The instrument is used as follows: A 10-foot pole is set against 
the tree. The observer stands at a convenient station whence he can see the tip and 
base of the tree and also the top of the 10-foot pole. The instrument is .suspended 
before the eye and moved back and forth until the edge b is in line of vision to the 
top of the tree and the edge c in line of vision with the base. The point where the 
line of vision from the eye to the top of the 10-foot pole intersects the inner edge 
of the instrument indicates on the scale the height of the tree. 



244 



THE MEASUREMENT OF STANDING TREES 



O 







Each instrument is constructed for use with a specified length of pole. The 

instrument described above is one designed by the author for 

convenience with the use of English units. It was constructed 

in the following way: The distance be on the instrument was 

chosen arbitrarily as 15 inches and the length of the pole as 10 

feet. It would, of course, be possible to construct an instrument 

for a pole 12 feet or any other length and on a basis of any 

desired length of instrument. The theory of the construction of 

Christen's instrument may be shown by Fig, 52. When used as 

above described, two pairs of similar triangles are formed: ABC, 

bcXDC bcXDC 

and Abe; ADC, and Adc, in which BC = and dc = . 

de BC 

With a known value of DC and be, dc may be determined for all 

different heights which are Ukely to be required. Thus it may be 

assumed that it would not be necessary to measure trees less than 

20 feet high, so that the lowest graduation on the instrument is 

made for that height. To find the proper point for the 20-foot 

graduation on the scale, the following formula was used: 



BC 


be 




20 


15 





zi 


or 


= 


=: 


DC 


dc 




10 


de 



or de = - 



= 5.7 inches 




FiQ. 51.— The 
Christen hyp- 
someter. 




Fig. 52. — Method of application of the Christen hypsometer. 



THE TECHNIQUE OF MEASURING HEIGHTS 245 

This same method was used to determine the value of dc for a 25-, 30-, 35-, 
40-foot tree, etc., up to 150 feet, and the proper graduations made on the scale. 
The scale is somewhat more easily read when a notch is made at each graduation. 

The instrument is light and compact, and with practice can be used very rapidly, 
provided one has an assistant to manage the 10-foot pole. It requires no measure- 
ment of distance from the tree, and the height is obtained by one observation. 
It is more rapid than either the Faustmann or Weise instrument. 

Its disadvantages are that it requires a very steady and practiced hand to secure 
accuracy, that it cannot be used accurately for tall trees, and that it is not adapted 
for steady work because it is extremely tiresome to hold the arm in the position 
required. This last objection may be overcome by using a staff to support the 
hand. 

199. The Technique of Measuring Heights. In rough checks for 
timber cruising, the distances used in obtaining heights are usually 
paced. Care must of course be taken to carefully check the paced 
distance desired to avoid incurring a cumulative error. For the measure- 
ment of average trees, depended upon to secure the heights of stands, 
the distance should, if possible, be measured with the tape. This 
latter method is the only one permissible in measuring the heights 
of trees on permanent sample plots. 

By the method illustrated by the Klaussner hypsometer, this dis- 
tance is measured along the ground whether the slope be leVel, gradual 
or steep. By the method of right triangles the distance must be meas- 
ured horizontally to the bole of the tree, and a considerable error would 
be incurred in measuring it along the surface on very sloping ground. 

Since the entire basis of the similar triangles used assumes that the 
tree which forms one side of the larger triangle stands in a vertical 
position, the consequences of measuring a tree which leans either towards 
or away from the observer are very serious (Fig. 53) . 

From the position A, the distance to the base of the tree is AC. 
But if the observer sights at the tip of the tree Bi which leans towards 
him, its height, when compared to the distance AC will be read as B'lC, 
an error of +16 per cent. If the distance is measured instead to the 
point directly below the tip Bi the height is read as BiCi, with an error 
of — 2 per cent. Again, if the tree Bo leans away from the observer, 
and its distance is measured as AC, its height will be read as B'iC with 
an error of — 16 per cent, but if this distance is measured to the point 
C2, the height will be read as B2C2 with an error of —2 per cent as 
before.^ 

If it is necessary to measure leaning trees, this can be done by taking 
a position at right angles with the line AC in Fig. 53, or at right angles 
with the vertical plane in which the tree lies. The ocular measure- 

' Some New Aspects Regarding the Use of the Forest Service Standard Hyp- 
someter, Hermann Krauch, Journal of Forestry, Vol. XVI, 1918, p. 772. 



246 



THE MEASUREMENT OF STANDING TREES 



ment of heights largely avoids this specific error since the eye 
allows for the leaning position of the tree while the instrument 
does not. 

Where total heights are measured to the tip of the crown, the 
greatest accuracy is obtained in the measurement of conical-crowned 
conifers. Broad- or deliquescent-crowned trees are difficult to measure 
accurately. The source of error is the same as that which applies to 
leaning trees. A line of sight AB, in order to be directed at the tip 
B, must penetrate the foliage of the crown while if directed tangential- 

ly to the edge 
of this crown, 
it will take 
the position of 
ABi. The error 
from the meas- 
urement of broad- 
crowned trees, 
unless this pre- 
caution is ob- 
served, is cumu- 
lative and tends 
to over-estimate 
their heights. 
Merchantable 

Fig. 53. — Errors which may be incurred in measuring the heights are meas- 
height of a leaning tree. To avoid error the measurement ured by exactly 
should be taken at right angles to the plane in which the the same princi- 
tree falls. pjgg ^^g g^j.^ g^p_ 

plied to total 
heights, and upon broad-crowned trees may be obtained more 
exactly. The element of uncertainty in the measurement of mer- 
chantable bole is not height, but the determination of the point 
on the bole at which the used length will terminate, that is, the 
merchantable top diameter of the bole. Merchantable heights may be 
measured in 16-foot log lengths by the use of the principle in Fig. 43. 
(Merritt hypsometer, § 195.) This same principle may be more accu- 
rately applied by leaning a pole of known length against the tree and 
then noting the length of a pencil required to take up this given length at 
the distance of the observer. This pencil length may then be measured 
off by eye on the remainder of the tree to divide it up into logs. 

It is common practice amongst timber cruisers to measure the 
total or merchantable height of windfalls as a check on ocular timber 
estimating. 




MEASUREMENT OF UPPER DIAMETERS. ^ DENDROMETERS 247 



200. The Measurement of Upper Diameters. Dendrometers. 

Upper diameters of standing trees must be measured, first, in estimating 
timber to a merchantable top diameter; second, to determine the form 
quotient of the tree, where form classes are to be distinguished. 

In timber estimating, ocular methods are used entirely, and the 
probable upper diameters approximated by knowledge of rates of taper 
checked by the measurement of diameters on the boles of down trees. 
But for the measurements required to determine form quotients, it is not 
safe to depend altogether on chance windfalls, nor can cutting sample 
trees be resorted to on account of the time and expense involved. The 
eye is not sufficiently accurate to gage diameters at upper points, hence 
these measurements for form quotient must be taken on standing trees 
by instrumental means. 

An instrument intended to measure the upper diameters of stand- 
ing trees is termed a dendrometer. 

The principle of the dendrometer is that of similar triangles; but in this case 
two sets of triangles are used, first, those required in determining the height to the 
point to be measured, 
and second, those 
used to measure the 
diameter at this point 
by comparison with 
the side of a smaller 
triangle on the 
dendrometer. These 
principles are illus- 
trated in Fig. 54. 

In determining the 
form quotient for 
standing timber, 
either according to 
Jonson's or Schiffel's 
methods, the diam- 
eter at the middle 
point, either above 
D.B.H. or above the 
stump respectively, 
is sought . As point- 
ed out, the absolute 
form quotient cannot 

be determined with scientific accuracy from measurements taken outside the bark 
or on standing timber, but approximate results can be obtained. 

The triangles whose bases are respectively B, 6i and 62 are similar, and the 
relation between B and either bi or bo determines the diameter at B. But the 
points 61 and 62 are not the same, and this difference distinguishes two different 
principles used in constructing dendrometers. 

When the distance Ac to the horizontal scale on which will be read the upper 
diameter B, is fixed, so that on sighting at point B this distance coincides with 62, 



jif III 

y^ 'i /III 

A^^ ± / I !c| 



Fig. 54. — Principles underlying construction of dendrom- 
eters, as illustrated by the Biltmore pachymeter. 



248 THE MEASUREMENT OF STANDING TREES 

as it does on most dendrometers, the proportion between the upper diameter B and 
its equivalent C, corresponding to c on the instrument, is aUered since the side Ab 
remains of the same length and coincides with ^4^2 in the figure. This discrepancy 
increases in proportion to the cotangent of the angle A and the distance read on the 
dendrometer scale at 62, which is graduated for inches, will be less than the true 
diameter B by just the amount of this error. The use of all dendrometers built 
on these j)rinciples requires correction by a table, to obtain true upper diameter. 

This difficulty is illustrated by a dendrometer attached to the Barbow cruising 
compass, used to some extent on the Pacific Coast. The dendrometer on this 
compass was a brass scale 1 inch long, finely graduated to read the apparent diameter 
m inches at the upper end of the <lesire(l log, when held exactly 1 foot from the 
eye by means of a string. But the true diameter had then to be looked up in a 
table furnished with the compass. The correction varied with the angle of sight; 
that is, with the number of log lengths in the. tree. All readings were made at 
100 feet from base of tree. 

On the Pacific Coast a second plan has been adopted, that of making the length 
of the scale ?>i equal to the diameter B, thus substituting two parallel lines of sight 
for the horizontal triangles shown, and reading the diameter of the lower side of a 
l)arallelogram directly in terms of inches of diameter at B. In an instrument 
invented by Judson F. Clark and C. A. Lyford, a telescopic sight moves on a bar. 
In one invented by Donald Bruce, both lines of sight are brought into the same 
plane by means of two reflecting mirrors, set at exact angles of 45 degrees. 

201. The Biltmore Pachymeter.' By employing the second principle, in which 
the side of the small triangle biC remains vertical, the diameter indicated at 61 
on the hypsometer remains in the same proportion to that desired at B, as when 
the reading is taken at position C. Since the point opposite c may be taken at 
the base of the tree, regardless of whether this point is horizontally opposite the 
eye or above or below it, a projection of the diameter B upon the base of the tree 
enables it to be directly measured on the tree, or on a scale c upon the instru- 
ment, graduated for the distance Ac. This principle is employed by an instrument 
termed the "Biltmore Pachymeter.'' (Ref. Forestry Quarterly, Vol. IV, 1906, 
p. 8.) A slot, the two edges of which are absolutely parallel, or a stick or cane 
of which the same is true is suspended in a vertical position in front of the eye. 
A scale marked in inches is held by an assistant tangentially to the tree trunk at 
D.B.H. The diameter at any desired point on the stem is obtained by finding the 
distance from the tree at which the diameter of the slot or stick exactly obscures 
that of the tree at the desired point, when the width corresponding to this diam- 
eter will be indicated by the intersections of these edges on the scale below. The 
instrument and its projection upon the tree trunk are shown in Fig. 54. 

202. The d'Aboville Method for Determining Form Quotients. This method 
depends on the measurement afb;, but is simplified by using a horizontal line of 
sight from eye to tree, and an angle of 45 degrees at point A, in which case the 
proportion between the lines AC and AB in Fig. 54 becomes 1.4, and the diameter at 
B becomes 1.4^2. To make this measurement, a distance is found which is just 
equal to the length of the bole between the point horizontally opposite the eye, as 
in Fig. 54, and the upper point to be measured. 

Substituting d and D for diameter at 5 height and D.B.H. respectively, the 
form quotient of a tree, as read on the dendrometer, is 

d 
/ = -Xl.4. 
D 

1 Pachyineter — an instrument for measuring small thicknesses. — Century Dic- 
tionary. 



/ 

THE JONSON FORM POINT METHOD 249 

The instrument consists of a graduated scale or straight-edge. For determining 
merely the form quotient the actual diameters need not be as^rtained but only 
their proportion or relation. The two measurements are taken by eye, holding the 
horizontal scale at arm's length {Ac and ^62) for each reading. The principal 
error to be guarded against is failure to secure the horizontal line of sight and the 
corresponding distance, which will residt in correspondingly large errors in reading 
the proportional diameters. Failure to select the right point on the tree, provided 
a definite point is selected and the method otherwise properly applied, incurs only 
the error due to difference in taper between the point measured and the point 
desired, which depends on rapidity of taper. 

This simple method should be of great assistance both to practical woodsmen 
in determining upper diameters, and to foresters desirous of testing the form quotient 
of trees in order to ascertain the applicability of volume tables based upon principle 
of form factors. 

203. The Jonson Form Point Method of Determining Form Classes. In con- 
nection with his studies of the form of trees and form quotients, Tor Jonson has 
evolved a method for determining the form class of standing trees without the 
necessity of measuring the upper diameter or the form quotient. 

This method consists in locating a point on the stem of the tree, which he terms 
the form point. The percentage relation which the height of this point from the 
stump bears to the total height of the tree, he claims, bears a consistent relation 
to the form quotient, and by means of a table showing these relations the form 
quotient and form class of the tree may be determined. 

Mr. Jonson describes the method as follows: 

The shape and position of the crown has been found to be the most dependable 
and useful indication of different tapers and form classes. This is connected with 
the bole's function to carry and steady the crown, especially against the breaking 
forces of the wind, and it has been found that in the building of the bole only 
enough material is used to make it equal in strength to the force of the winds. It 
may therefore be said that it is the strength of the winds that determines the 
necessary dimensions of the trunk, and as the force of the wind is generally applied 
to the crown of the tree, it will be found that its weight, shape and position indirectly 
influence the size and taper of the trunk. 

While estimating, the D.B.H. is measured with caliper and the taper is then 
determined through finding by ocular means the form point, i.e., the point where 
the pressure of the wind is apparently concentrated which is usually the geomet- 
rical center of the crown. By sighting at this point and at the same time at the 
base and tip of the tree over a stick, approximately 30 cm. long, divided into 10 
equal parts (Christen's hypsometer), the height of the form point can be easily 
fovmd expressed in per cent of the total height. This form point can then be 
looked up in the table giving the form point heights which are characteristic for 
each form class. The higher the crown is placed, the less the taper and the more 
cyhndrical the form, and conversely, the lower the crown extends, the more rapid 
will be the taper and the poorer the form. 

When, as is often the case, the estimating is based on diameter outside bark, 
the difference which is caused by variable thickness of the bark must be taken 
into consideration. The spruce, fir and other species with thin even bark show 
no difference in form when measured inside or outside bark, for which reason the 
given normal form point heights give the form with, as well as without, the bark 
for these trees. 

White birch, larch and others, but especially the pine, show great reduction in 
form when measured with bark, for which reason the form quotient outside bark 



250 



THE MEASUREMENT OF STANDING TREES 



is different from what the crown normally signifies. On this account special tables 
have been made up for use with outside bark measurements, but, as the Scotch pine 
shows many different types of bark, four tables have been compiled for trees whose 
bark is thin, medium, thick and very thick. 

When judging the location of the form point, it should be remembered that it 
is at the base of the branches where the acting forces of the wind are transferred 
to the bole, for which reason deciduous trees with branches pointing up will have 
the form point not in the center of the crown contour but as much lower as the 
bases of the branches he lower than the foliage on which the wind is acting. In 
estimating trees which have quickly cleared themselves of branches, a better result 
will be obtained, if the newly shed crown be imagined reconstructed before the 
position of the form point is determined. 

Finally, should the butt swelHng extend so high as to influence the D.B.H., 
and consequently make the final result inaccurate, it will be satisfactory for prac- 
tical work either to roimd the diameter off downward or measure the diameter 
above the swelhng; for scientific work, however, the form class should be lowered 
as much as is made necessary by the butt swelling, which can be easily found through 
a number of measurements taken above and below B.H. 

In extensive timber estimating the density is a good indication of the general 
form which the trees ought to possess, as the tree grown up in dense stands will 
have a clean bole and high crown, while on the contrary the tree grown in the open 
will have a heavy, low crown and consequently a poor bole form. 

TABLE XL 

Table for Determination of Form Class of Trees by Means of Position of 

Form Point ^ 



Height 


Form Class 


of 




1 
















1 


tree 
in 


0.50 0.525 


0.550.575 


0.60 


0.625 


0.65 


0.675 


0.70 


0.725 


0.75 


0.7750.80 


feet 


Form point height in per cent of height of tree 




10 


37.5 


43.5 


47 


52 


57 


62 


69 


73 


79 


85 


92 


98 




20 


35.5 


40 


44 


49 


54 


59 


65 


70.5 


76.5 


82.5 


89 


95.5 




30 


34.5 


38 


43.5 


47.5 


52.5 


58 


63.5 


69 


75 


81 


87 


94 




40 


34 


38 


43 


47 


52 


57 


62 


68 


74.5 


80 


86 


93 




50 


34 


38 


42.5 


47 


52 


57 


62 


68 


74 


80 


86 


93 




60 


34 


38 


42 


47 


52 


57 


62 


68 


73.5 


80 


86 


92.5 




70 


34 


38 


42 


47 


52 


57 


62 


68 


73.5 


79.5 


86 


92 




80 


34 


38 


42 


47 


52 


57 


62 


68 


73 


79 


86 


92 





" For spruce and fir in Norway, either inside or outside bark. Adapted from 
Massatabeller for Traduppskatnung. Tor Jonson, Stockholm, 1918. 

The prevailing density of a stand causes the greater number of the trees to acquire 
a certain similarity as to form, and only a very small number, usually the smallest 
and largest trees, differ from this average form class. Accordingly it is often 



1 



RULES OF THUMB 251 

204. Rules of Thumb for Estimating the Contents of Standing Trees. 

A rule of thumb represents an attempt to formulate a simple rule which 
can be memorized and by the use of which the contents of trees of any 
diameter and height may be found. Such a rule would enable the 
cruiser mentally to compute the volume of average trees without looking 
them up in a table. It is also desired as a substitute for a universal 
volume table because of the difficulty of finding volume tables for the 
different species. 

The factors of variation in tree form are exaggerated by application 
of units of product and the variation in board-foot log rules, and the 
further differences in the per cent of total contents utilized in trees of 
different sizes make it impossible to devise rules of thumb w^hich are 
as accurate as good volume tables; but since their use in ocular timber 
estimating frequently accompanies methods of cruising by which a 
close degree of accuracy is not attained, a slight possibility of error 
in application is not considered a sufficient drawback to offset the 
advantage of simplicity. They are especially desired in judging by 
eye the contents of single trees. 

Rules of thumb must be based upon either the cubic or board-foot unit. The 
simplest forms ignore the influence of height and are therefore inaccurate except 
when applied to trees within a given range of heights. 

The effort is always made to devise rules which may be applied to the dimensions 
measured by the eye; that is, to diameter and height. Rules which require the 
use of basal area call for tables. 

For cubic contents, the following rules of thumb will serve as illustrations: 

1. To obtain cubic feet multiply the basal area in square feet by the height 
and divide by 2. This is based on the theory that the cubic form factor of trees 
will average 0.5 which is the form factor for a paraboloid. 

2. For trees averaging 80 to 100 feet in height, with a form factor of 0.49, the 
contents in cubic feet equals the radius in inches squared (B. E. Fernow). For 
"average" trees, volume in cubic feet equals one-fifth of the diameter squared 
(C. A. Schenck). 

Both of these rules of thumb are good only for trees of a given height and form 
factor. They are similar to the European rule of thumb — volume in cubic meters 
equals the diameter squared divided by 1000. In this rule, D is measured breast- 
high in centimeters. This rule applies to pine 30 meters high, beech, oak and 
spruce, 26 meters high, and correction factors are indicated as follows: for 
each additional meter of length above or below these heights, for pine, a 3 per cent 
correction; for beech, 5 per cent; for spruce and fir, 3§ per cent. Hersche's rule 

(h \ 
of thumb reads, cubic meters = 1)2 1 --[-1 1, using meters. This applies to trees 

50 to 115 feet in height. \^ I 

possible to estimate the whole stand in the same form class, the smaller dimensions 
a little higher and the larger dimensions somewhat lower than the average, e.g., 
0.70 for overtopped trees, 0.675 for intermediate and co-dominant trees, and 0.65 
for dominant trees (§ 171). The highest and lowest form classes will never occur 
as an average, but only for single trees. 



252 THE MEASUREMENT OF STANDING TREES 

Graves gives the following cubic rule of thumb for white pine; 

Square the breast-high diameter in feet and multiply by 30. The rule gives 
approximately correct results for trees 10 to 14 inches in diameter and 80 feet 
high, 16 to 20 inches by 85 feet, 22 to 28 inches by 90 feet, and 30 to 36 inches by 
95 feet. Other heights require a correction varying between 5 and 6 per cent, 
for each 5 feet of length. It can thus be seen that both simplicity and accuracy in 
these rules of thumb are seldom obtained in the same formula without considerable 
cumbersome modification and it would seem that a volume table could be referred 
to almost as easily and give as accurate results. 

The use of rules of thumb based on board feet is primarily caused by lack of 
suitable volume tables. This is illustrated by the development of rules of thumb 
based upon the Doyle log rule. These board-foot rules are efforts to obtain the 
total board-foot contents of the trees from the sum of the contents of the logs which 
they contain and were usually formulated before volume tables had come into use. 

The simplicity of the formula for obtaining the contents of a given log in the 
Doyle rule, namely, "subtract 4 inches from the upper diameter inside bark, square 
the remainder, and the result is the scaled contents of a log 16 feet long" (the length 
used in estimating), was an inducement to supplement this rule so as to obtain 
the contents of the average log in a given tree. There are two rules for this. 

1. Take the average diameter of the top and stump inside the bark for the 
diameter of the average log. Scale this and multiply by the number of 16-foot 
logs in the tree. 

2. Multiply the diameter at breast-height inside the bark by the same diameter 
minus 12. Multiply by the number of logs in the tree. This gives the scale of 
the tree (C. A. Schenck). 

Schenck also gives a rule which ignores height, as follows: For "tall" trees, 
volume = iy diameter squared, measured at breast-height. 

Efforts to formulate general rules of thumb, not based on the Doyle rule are 
illustrated by the following examples: 

1. Subtract 60 from the square of the estimated diameter at the middle of the 
merchantable length of the tree. Multiply by 0.8 and the result is the contents 
in board feet of the average log in the tree. Multiply by the number of 16-foot 
logs for the total scale. (Graves' Mensuration, p. 153.) 

2. Average the base diameter of the tree and the top diameter of its merchant- 
able timber. Get the scale of a log of that diameter, 32 feet long. Multiply by 
the number of 32-foot logs less | log. (Gary's Manual of Northern Woodsmen.) 



3. Board f eet ^ 



60 



when D = inches and L = feet. 

(A formula method of estimating timber, E. I. Terry, Journal of Forestry, 
Vol. XVII, No. 4, p. 413.) This formula, according to author, requires modification 
by substitution of a divisor of 

70 for trees from 12 to 19 inches D.B.H. 
60 for trees from 20 to 29 inches D.B.H. 
55 for trees from 30 to 35 inches D.B.H. 
50 for all trees above 35 inches. 

4. To base diameter, add one-half of base diameter and divide by 2; multiply 
by 0.8, square and divide by 12. The result is the number of feet in the stick per 
foot of its length. Three to 5 per cent may sometimes be added for contents above 
the point stated. 



• RULES OF THUMB 253 

There are two steps involved in these rules of thumb for board feet: 
First, a rule or formula is required, which gives an approximation of actual 
board-foot contents of logs of different sizes. This can only be obtained by rules 
based on cubic instead of board-foot contents (§ 39). Taking a fixed per cent of 

the contents of all logs, the last rule above quoted reduces to ( 

The second step is to get the dimensions of an average log in a tree, thus averaging 
large and small, or top, butt and middle logs together. Empirical results rather 
than mathematical soundness has usually been the basis of all such rules of thumb. 

Practically all these rules of thumb for board feet are based upon the log unit, 
as might be expected. A more scientific application of a universal rule of thumb 
is that devised by F. R. Mason (Ref. Rules of Thumb for Volume Determination, 
Forestry Quarterly, Vol. XIII, 1915, p. 333). This rule is as follows: 

5. The volume of a tree of each diameter and height class will correspond 
closely with the volume as obtained by averaging the scale of the butt and top 
logs and multiplying by the number of logs, using 16 feet as the standard log length. 

Mason states that this rule has been in use by Minnesota cruisers. Its superior 
accuracy is based upon the fact that it conforms to the form quotient of the tree 
as well as to its diameter and height, by introducing upper diameters at two points. 
For Douglas fir this rule was 3 per cent below actual scale; for cedar, above 24 inches, 
10 to 15 per cent high. For white pine, spruce, yellow pine, larch, lodgepole pine 
and fir, average results were within 5 or 6 per cent of actual volume for individual 
trees of all sizes, a result which is closer than may be expected in the use of average 
volume tables for single trees. The only difference between this rule and the tally 
and computation of each log in the tree is elimination of the need for tallying logs 
lying between butt and top. The size of the top log is constant where a fixed top 
diameter is used. Mason states that 3R^ is the approximate board-foot contents 
for 16-foot logs over 24 inches in diameter. 

6. A rule given by J. W. Girard is, "add 6 inches to the D.B.H., divided by 2 
and use this result as the diameter for the average log in the tree. Multiply the 
scaled volume of this log by number of logs for the tree volume." This rule holds 
good for white pine and spruce cut to 6-inch top and for larch cut to 8-inch top. 
For Douglas fir cut to 8-inch top, add 4 instead of 6 inches. For lodgepole cut to 
6-inch top, add 5 inches. For yellow pine under 20 inches, add 6 inches; 20 to 25 
inches, add 8 inches; 26 inches and over, add 10 inches. 

Any rule of thumb should be based upon the log rule and standard of utilization 
in use. Such rules are largely worked out as a matter of personal efficiency by 
individuals and should be tested carefully before placing too much reliance upon 
them. 

References 

The Biltmore Stick and Its Use on National Forests, A. G. Jackson, Forestry 

Quarterly, Vol. IX, 1911, p. 406. 
Notes on the Biltmore Stick, Donald Bruce, Proc. Soc. Am. Foresters, Vol. IX, 

1914, p. 46. 
The Biltmore Stick and the Point of Diameter Measurements, Donald Bruce, Proc. 

Soc. Am. Foresters, Vol. XI, 1916, p. 226. 
A Folding Biltmore Stick, W. B. Barrows, Journal of Forestry, Vol. XVI, 1918, 

p. 747. 
Relative Accuracy of Cahpers and Steel Tape, Normal W. Sherer, Proc. Soc. Am. 

Foresters, Vol. IX, 1914, p. 102, 



254 THE MEASUREMENT OF STANDING TREES 

Another Caliper (Swedish pole and hook for measuring diameters at considerable 

height). S. T. Dana, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 337. 
Saving Labor in Measuring Heights, S. B. Detwiler, Forestry Quarterly, Vol. XIII, 

1915, p. 442. 
A New Hypsometer, H. D. Tiemann, Forestry Quarterly, Vol. II, 1904, p. 145. 
Comparative Test of the Klaussner and Forest Service Standard Hypsometers, 

Douglas K. Noyes, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 417. 
Some New Aspects Regarding the Use of the Forest Service Standard Hypsometer, 

Hermann Krauch, Journal of Forestry, Vol. XVI, 1918, p. 772. 
A Simple Hypsometer, Vorkampff Laue, Forestry Quarterly, \'ol. Ill, 1905, p. 195. 
A New Dendrometer, Donald Bruce, University of California Publications, Vol. Ill, 

No. 4, Nov., 1917, pp. 55-61. Review, Journal of Forestry, Vol. XVI, 1918, 

p. 724. 
A New Dendrometer or Timber Scale, Judson F. Clark, Forestry Quarterly, Vol. XI, 

1913, p. 467. 
The Biltmore Pachymeter, Ralph G. Burton, Forestry Quarterly, Vol. IV, 1906, p. 8. 
Determination of the Middle Diameter of Standing Trees, P. d'Aboville. Trans- 
lation, Journal of Forestry, Vol. XVII, 1919, p. 802. 
Rules of Thumb for Volume Determination, F. R. Mason, Forestry Quarterly, 

Vol. XIII, 1915, p. 333. 
A Home Made Hypsometer (Winkler t>7)c). Construction described in Farmers 

Bulletin 715, 1916, p. 18. 



CHAPTER XIX 

PRINCIPLES UNDERLYING THE ESTIMATION OF STANDING 

TIMBER 

205. Factors Determining the Methods Used in Timber Estimating. 

There are five basic considerations which determine the conditions 
and methods to be used in estimating timber. These are: 

1. The form of product in wliich the vohmie of the timber is to 
be estimated. This determines tlie unit of volume to be used, as the 
piece (poles, railroad ties), the board foot for saw timber, and the cord 
for bulk products (§§ 9-12). 

2. The economic conditions, customs and usages governing thr> 
business of logging and lumbering. These determine the basis on 
which standing timber is to be sold and the place and form in which 
it is to be measured. The three considerations which affect the work 
are, whether the basis of volume measurements is to be the contents 
of logs or the sawed output in the form of lumber, what log rule is to 
be used in scaling the logs, and the practice of scaling as to log lengths, 
diameters and cull as affecting the scaled contents of the timber 
(§§81-83). 

3. The character of the demand for timber products and the result- 
ant closeness of utilization of the trees in the stand. This will determine 
the top diameters and stump heights to which the timber must be esti- 
mated, and the minimum D.B.H. (diameter limit) of trees to be esti- 
mated as part of the merchantable stand, and consequently the per cent 
of the total cubic volume of the stand which is estimated as merchant- 
able (§23). 

4. The available volume tables, their reliability and basis of numbers, 
their method of construction, their basis of diameter, height and mer- 
chantable top diameters (§ 124). This will determine, 

(a) Whether to dispense with a volume table and substitute a 
log rule, tallying the contents of the trees in the form of 
separate logs or to depend upon a volume table for entire 
trees. 

(6) The point at which diameter must be measured in timber 
estimated, as stump, D.B.H. , or top of first log inside 
bark. 

255 



256 ESTIMATION OF STANDING TIMBER 

(c) The point at which heights are taken — total height o r 

merchantable log length. 

(d) The top diameters to which tree must be estimated. Diver- 

gence in these conditions from those used in the volume 
table will make it impossible to apply the same. 

5. The local characteristics of the timber to be estimated as to full- 
ness of form or " form quotient," quality and defects. This determines, 

(a) For sound trees, the applicability of existing volume tables 

without modification or their need of local percentage 

corrections, 
(fe) For the defective trees, the amount of deduction for defects 

and losses in scale to be made from the standard volume 

table. 

The object of any estimate of standing timber is to obtain the total 
volume as indicated by the above five conditions upon the entire area 
of a specific tract of land. This may be done in one of three ways: 

By direct ocular guess or appraisal. 

By actual estimate or measurement of the volume of every tree 

of merchantable size. 
By measuring or estimating a part of the timber as an average 

.of the whole. 

206. Direct Ocular Estimate of Total Volume in Stand. The direct 
estimation or guess of the total volume of a tract of timber can have 
but one basis, that of experience in cutting tracts of similar character. 
This eliminates all doubtful factors, and the experience thus gained 
is invaluable as a standard of estimating. 

Skill and accuracy in this method depend upon the uniformity of 
the stand, and the ability of the estimator to compare this uniform 
stand with those of similar character whose yield he has ascertained. 

As the area of timber so estimated incr ases, its variability of 
stand becomes greater; yet the necessity for obtaining a true average 
of these variable conditions persists. Even in stands as large as 40 
acres it becomes very difficult even with the closest inspection to arrive 
at the average stand on the tract, no matter how skillful the cruiser is 
for smaller and more uniform areas. With increasing size of area, 
accuracy soon becomes utterly impossible. For this reason, in spite 
of the simplicity of the plan in theory, in practice cruisers who depend 
solely upon this principle are apt to be unreliable and inaccurate. 
Under no circumstances can this method be applied to timber with 
which the cruiser is unfamiliar. It therefore limits his field of activity 
to a narrow basis. 



ESTIMATING A PART OF THE TIMBER 



257 



207. Actual Estimate or Measurement of the Dimensions of Every 
Tree of Merchantable Size. This is known as a 100 per cent estimate 
and differs radically from the total ocular estimate of stand just 
described. It consists of recording the dimensions of each log on the 
tract in case no volume table is used, or with a volume table, the dimen- 
sions of every tree of merchantable size. The total volume is then 
simply a matter of computation. 

The trees are tallied by dots and lines, in blocks of ten, as indicated 
in the following table, which shows the marks corresponding to dif- 
ferent numbers: 

1 3. 3d 5 6 7 8 9 10 

• ••'::: r. n n n H H 

When diameter alone is being tallied, a single column giving diameter 
classes suffices for each species. Where the height, either total or 
merchantable is also recorded for each tree tallied, each species will 
require a tally similar to 
that shown below. 

Where several species 
are tallied by both diameter 
and height, it is not cus- 
tomary to make half-log 
divisions, since too many 
columns would be involved. 
Where the top diameter of 
logs, instead of D.B.H., is Fig. 55. — Method of tallying trees by diameters 
the point talhed, the same ^^^^ log lengths. 

system of diameter classes 

or tallies is used. It is possible to combine this tally of D.B.H. for 
one species with top diameter of logs inside the bark for others, using 
the same horizontal columns for diameter in each case. 

208. Estimating a Part of the Timber as an Average of the Whole. 
Where the greatest possible accuracy .is demanded, it is obvious that 
100 per cent of the trees should be measured. Only in extreme cases 
can this be done, owing to the excessive cost. The process of measure- 
ment accomplishes no constructive change in the form of the forest 
(§ 6) as does logging or silviculture, but is of use merely in the orderly 
management of the business of regulating these operations as to location, 
quantity and time. Efficiency then demands the reduction of the cost 
of obtaining these statistics to the lowest figure which will suffice for 
the proper conduct of the business and avoid loss through errors in 
appraisals of quantities and values. 

With timber whose average value per tree is small, the cost of meas- 







Spec 


ies-Pine 






D.B.H. 


Hog 


2 logs 


2! 2 logs 


Slogs 


etc. 


12 












13 












14 




n 








15 













16 






: I 


r 




etc. 













258 ESTIMATION OF STANDING TIMBER 

uring each tree is far too great to be undertaken. It is often physically 
impossible to obtain the necessary force and personnel to perform the 
work on this scale. Finally, the time I'equired is too long since the 
results of estimates, especially for the purpose of sale are usually required 
within a limited period. For these reasons, the third of the above 
methods, by which the principle of averages is utilized as a means of 
reducing expense, diminishing the number of persons required and 
shortening the time demanded for completing the work, is almost 
universally used in estimating timber. 

The use of this principle in timber estimating does not differ from 
that applied in the commercial process of sampling employed in mines 
or in grad'ng wheat. If the product is uniform, a single sample suffices, 
as in wheat, but if variable, as in ore, far greater care is required in 
order that the samples may represent the average value for the entire 
body to be tested. The advantage in timber estimating is that all 
of the timber is actually visible and only the handicap of costs and 
time prevent it from being seen and measured. 

209. The Six Classes of Averages Employed in Timber Estimating. 
There are six classes of averages employed in estimating timber. The 
first three differ in regard to the methods of recording the dimensions 
of trees. These methods are as follows: 

1. The average height of the trees of each separate diameter class 
is obtained For this purpose, only a few sample heights for each 
separate diameter are measured. The heights so measured are plotted 
on cross-section paper on which diameter is the determinate variable 
plotted on the horizontal scale, while height is the indeterminate vari- 
able plotted on the vertical scale. 

An illustration of a curve to obtain average heights based on diameter is shown 
in Fig. 56. The trees to be measured for height must be selected in such a manner 
that the resultant curve will give the true average heights for each diameter class 
for the entire area to which it is to be applied. When a very few trees are taken, 
these must be carefully chosen from those whose crowns are of average height 
compared with the remaining stand. This is best accomplished in even-aged stands. 
On large areas and in many-aged stands, a mechanical distribution of trees measured 
for height is best, in order to secure a weighted average of differences caused by 
variation of site and of growth. 

In plotting the data, two methods are shown. By the first, all heights are 
plotted above their respective diameters. A height curve may thus be sketched 
by eye through the band of points shown. This eliminates mechanical averaging. 
By the second method, the average height is calculated for the trees in each diameter 
class, and this point is plotted 0. The points are then connected by straight 
lines, their weight in numbers shown, and the curve drawn, as before, guided by 
the original data.' 

1 In the first system, when two heights fall on the same point, the number is 
indicated as ^. 



AVERAGES EMPLOYED IN TIMBER ESTIMATING 



259 



A combination of these two systems may be used as follows: First plot the 
points, then compute the mechanical averages from the plotted data by using the 
scale as follows: For the 9-inch trees, assume the 40-foot point as 0. The 
trees are then entered as having the weights 0, 3, 8, 8; total 19; average 4.8 plotted 
as 5 above the 40-foot point, or an average height of 45 feet. This method com- 
bines the advantage of visuahzing the data to indicate abnormally high or low 
trees, with a slight reduction in the work of mechanical averages. 

2. Instead of tallying the diameters of all the trees, they are merely 
counted, but a certain fixed percentage of the total number is tallied 
for diameter (the heights are either tallied individually or the method 

70 



I 50 



tt 40 



30 





























/ 


K 






















j 




9 


/ 


^ 






















/ 


i^ 


r\ 


f 
















^ 


^ 


^ 


r 


















4j 


tJJ' 


^ 


2 


-s 


















A 


s 


/ 
























>* 


/A 


/ 


























/ 




. 
























" 3' 


h 



























































10 



11 12 13 
D.B.H. Inches 



15 IS IT 18 



19 



Fig. 56. — Method of constructing a curve of height based on diameter at B.H. 
White Pine, Milford, Pike Co., Pa. 



of averages described above is applied). The volume of the average 
tree of the per cent tallied is used to find the average volume cf the 
numbers counted but not measured. 

In Southern longleaf pine, it is possible to count all of the trees on a tract, 
and to tally the diameter and merchantable height of one tree in every three in 
such a way that the trees tallied represent the mechanical average of those counted. 
When the volume of the tallied trees is computed, it represents one-third of the 
volume of the stand. The work of tallying has been reduced one-third and the 
accuracy greatly increased, when considered with reference to the time required to 
complete the work. 

3. None of the trees in the stand is tallied for either diameter or 
height. The trees are merely counted and the cruiser then decides 
upon the volume which will be contained in the average tree of the stand. 
He may obtain this either through a direct guess as to volume or through 



260 ESTIMATION O-F STANDING TIMBER 

the selection of what he beheves to be a tree of average diameter and 
height whose volume he then ascertains. There are two modifications 
of this system, dependent upon whether the unit used is the log or 
the tree. When the log unit is used, the cruiser estimates the number 
of logs in the average tree and the contents of the average log or log 
run (§ 120). 

In the above three methods of averaging, nothing has been said 
about the question of area covered. The averages apply to that portion 
of the area on which the timber is either counted or in addition is tallied 
for dimensions. This may be 100 per cent or the total area. Although 
it may not be possible to measure, by diameter and total height, each 
tree on the entire area, yet by the employment of one of these three 
methods of averaging the contents, all of the trees may actually be 
accounted for. 

The remaining three of the six methods of employing averages 
apply to tracts whose area is too large to permit of 100 per cent esti- 
mates, even by the simplest plan of counting and obtaining the average 
tree. The principle here is to estimate the stand on a portion of the 
area in an effort to derive the volume of the stand upon the remainder. 
The systems used are as follows: 

4. The stand per acre is guessed at or estimated by eye. This stand 
multiplied by the area in acres presumably gives the total stand on the 
tract. This is merely a modification of the method of total ocular 
estimate, in which the problem of arriving at the average is approached 
in a different manner. It is possible for a skilled estimator to guess 
closely the stand on a given acre, but the difficulty lies in either finding 
a specific stand whose volume per acre happens to agree with the aver- 
age on the entire tract or else to decide from the inspection of given 
stands how much the actual stand per acre observed on specific plots 
must be modified in order to obtain the true average for the entire 
tract estimated. The probabilities of error in estimates made on this 
basis increase with the size and diversity of the stand to be estimated. 

5. The dimensions and volume of the trees on a given per cent of 
the total area are obtained b}^ one of the first three methods and the 
stand thus found is assumed to represent the average stand per acre 
for the entire tract. This requires, fii'st, the accurate determination 
of the area of the tract and of the area covered by the estimate, and 
second, the location of this latter area in such a way that the assumption 
that it represents the average of the remainder can be accepted as 
approximately correct. 

6. The same principle is employed as described under 5, but the 
assumption that the per cent of area so measured will give an accurate 
mechanical average applicable to the remaining tract is not accepted. 
Instead, the remainder of the area is inspected by the method of ocular 



THE CHOICE OF A SYSTEM FOR TIMBER ESTIMATING 261 

comparison. None of the trees is actually measured except on the 
per cent estimated. Using this estimated strip as a standard, the 
estimate upon the remainder is taken as equaling, exceeding or falling 
short of the stand per acre upon the estimated strip, and its volume 
is obtained by applying a correction to this estimated stand per acre. 
210. The Choice of a System for Timbej Estimating, with Relation 
to Accuracy of Results. All systems of timber estimating involve the 
choice, first, of one of the three methods for determining the contents 
of the trees and second, of one of the three methods of covering the area. 
There are many different systems of timber cruising, involving the 
possibility of an endless combination of these six elements Each of 
these systems represents a decision as to the per cent of area required 
to get the average stand per acre for the total area, the method of cover- 
ing the area to obtain this per cent, and the question as to acceptance 
or modification of the stand per acre as applicable to the whole tract; 
it also involves the further reduction in the work of measuring dimen- 
sions to get the volume of trees by substituting averages for height, 
a per cent of total tallies for total tallies and average volumes for 
individual volumes. These two groups of factors are closely inter- 
related. For instance, where the per cent of area covered is reduced 
to a low figure, the area which is actually estimated must be covered 
thoroughly by careful measurement of distances and widths of strips, 
the diameter of every tree should be measured or tallied, and each tree 
may be tallied for height, especially if merchantable heights are used. 
Where, on the other hand, all of the area is covered, it may be sufficient 
merely to count the trees, substituting the method of an average tree 
or log for the more detailed and time-consuming method of measuring 
each diameter. The gain in accuracy in one of these factors may be 
offset against possible inaccuracy in another, the sum of the factors 
being determined by the total cost of the method. These points may 
be briefly summed up as follows: 

Area — 

Full estimate, 100 per cent. 
As modified by averages. 

Sample plots taken as the average. 
A given per cent accepted as the average. 

A given per cent estimated as a basis for obtaining the remainder by compari- 
son and correction. 
Trees — 

Full estimate, 100 per cent tallied for both diameters and height. 
As modified by averages. 

Average height obtained from sample measurements. 

Volume of average tree obtained from tally of dimensions of a fixed per cent 

of the total stand. 
Volume of average tree obtained by inspection, from s.-miplc tree, or average 
tree on sample plots. 



262 ESTIMATION OF STANDING TIMBER 

Both the degree of accuracy obtained and the expense of estimating 
the timber are reduced: 

By the reduction of the per cent of area covered. 

By substituting tree counts for measurements of dimensions and 
averages for totals. 

By substituting ocular measurements of dimensions for instru- 
mental measurements. 

By substituting pacing for chained or measured distances. 

As an offset to the loss of absolute accuracy by the substitution of 
these laws of averages and reduction of detail, the relative accuracy 
or efficiency of the application of the cheaper methods can be enormously 
increased by the development of technical skill, experience and judg- 
ment, so much so that the old-time timber cruiser depended upon these 
factors both for his reputation and the reliability of his estimates. 
This relative accuracy is increased: 

By the choice of methods and care in location by which partial 
areas are secured in such a manner as to insure the highest probability 
of average volumes. This is similar to the methods used in sampling 
ore. 

By the development of skill and accuracy in the use of pacing 
and in the use of the eye for measuring diameters, heights and width 
of strips or plots. 

By the ability to apply the methods of tallying a fixed per cent of 
the stands or selecting average trees in such a manner that the true 
average volume of the total number or count is obtained. 

By painstaking observance of obtainable standards of accuracy in 
the use of instruments for measuring distances, diameters and heights, 
and in proper record or tally. 

By individual training and ability to make the proper discounts 
for defects. 

By the careful checking of the reliability of volume tables used, 
and the correlation of field methods with the conditions for which they 
were constructed. 

Finally, by correlating all of the above factors with the actual con- 
ditions of the tract or stand to be estimated, which in themselves will 
determined the degree of accuracy required in each step as above 
outlined. 

211. Relation between Size of Area Units and Per Cent of Area to 
be Estimated. There are two elements to be considered in arriving 
at accurate averages in estimating a given tract. First, the problem 
of distributing the samples throughout the area in order to obtain the 
greatest probability of true average; second, the uniformity of the stand 



SIZE OF AREA AND PER CENT OF AREA ESTIMATED 263 

itself as increasing or decreasing the probability of accuracy for a given 
method of sampling. 

The first of these problems is influenced by the size of the tract. 
In any method of estimating based upon measuring a part of the area, 
the system employed must be that of strips or plots spaced at regular 
intervals. Otherwise the element of judgment in selection introduces 
a difficult factor which will improve the average obtained only when 
accompanied by considerable individual skill. With plots or strips 
at fixed intervals, the number of such strips depends upon the dimensions 
of the tract. 

The choice between plots and strips does not affect this principle. 
Plots, when substituted for strips and taken along compass courses at 
regular mechanical intervals, serve to reduce the per cent of total 
area covered. Since the distribution of the sample areas is more evenly 
diffused on the basis of the per cent covered, by plots, than it is by 
strips, the loss in accuracy by substituting plots for strips is not in 
proportion to the reduction in per cent of area covered, but is consider- 
ably less, thus resulting in a material saving where the use of plots 
permits of the reduction in size of crew (§ 224). 

The size of the separate units of area on which accurate estimates 
are desired — as for instance, when owners require the estimates sepa- 
rately by '' forties " (§8), is the basis for determining the effect of the 
spacing of these strips. If the estimate must be accurate only for the 
entire tract, a quite different problem is presented from that when the 
same degree of accuracy is required for smaller subdivisions. Assuming 
that the tract is in the form of a square, the coefficient of accuracy bears 
a close relation to the number of strips run across this area, rather 
than to the distance between these strips. This may be expressed as 
follows: 

The per cent covered by strips will be the product of the number 
of strips and width of each strip, divided by width of the area. With 
strips of a uniform width, e.g., 8 rods or 132 feet, run at intervals of 
I mile, the per cent of area covered is -^ or 10 per cent, whether the tract 
be 40 acres, 1 square mile or 25 square miles. But the probability of 
accuracy in securing an average stand is not in the same proportion 
for each tract, but increases with the size of the tract. The reason is 
that, regarded as a unit, the larger tract is more uniformly sampled, 
and with reference to its total area, the strips or plots are more 
thoroughly distributed than on the smaller areas. The relative accu- 
racy is in proportion to the distribution of the sampled or estimated 
strips with respect to this total unit, which for large tracts tends to 
reduce the per cent of area required to obtain a given standard of accu- 
racy. 



264 



ESTIMATION OF STANDING TIMBER 



Standard distances between strips or plots are 80 rods, or once 
across a forty for very extensive work of low accuracy; 40 rods, or 
twice across a forty for work of average accuracy; 20 rods, or four 
times across a forty for work approaching a 50 per cent estimate; 
10 rods, or eight times across a forty, which with a 10-rod strip 
permits 100 per cent of the timber is to be measured. 

The first problem then, in estimating a tract, is to decide upon the 
proper per cent of the area which must be covered to secure the desired 
standard of accuracy, and this per cent will be a direct function of the 
size of the smallest unit of area upon which a separate estimate is 
required (Fig. 57). 

25 Sqviare Miles 



1 Square Mile 



Va Sq.Mile 



1 r 

I I 
J L 



tr^ 



^ 






t-rH-r 






I ! ! 



•^ Mile 



Fig. 57. — Influence of size of tract upon probable error in obtaining average volume 
per acre, by running strips 40 rods apart in each instance. Dotted lines 
indicate location of strips. 



Narrow strips spaced at one of these standard intervals are commonly 
used for large tracts. Upon small tracts, the necessity for increasing 
the per cent of area covered, as a substitute for increasing the number 
of strips run, takes the form of widening the strip. This is usually 
accompanied by a modification of the method of tallying the trees 
and the substitution of a count for the measurement of every diameter. 
For small areas as low as 40 acres, this frequently takes the form of a 
100 per cent estimate, the strips being so arranged that they cover the 
entire area, and where the value of the timber and its size is such that 
accuracy is desired for each forty, 100 per cent of the entire tract is 
covered, no matter what its total size. 

The relations between the distance apart of strips or plots, width 
or size of these strips or plots, and resultant per cent of area covered, 
to the size of the unit of area to be estimated, is the most practical 



UNIFORMITY OF STAND AS AFFECTING METHODS 265 

problem of timber cruising upon whose solution depends the attain- 
ment of the desired standard of efficiency secured by properly relating 
costs to accuracy of results. 

212. Degree of Uniformity of Stand as Affecting Methods Employed. 
The second factor affecting the probability of accuracy in obtaining 
the average stand per acre is the character of the stand as affecting its 
uniformity. Uniformity depends, first, upon the range of sizes both, 
as to diameter and height of the trees which compose the stand; second, 
on the regularity or evenness of their distribution or the variation in 
the density of the stand over the area. The greater the extremes, 
both in sizes and density, the more difficult the attainment of a correct 
average stand by a measurement of a part of the area, and the greater 
the necessity of increasing either the number of strips or the per cent 
of area covered in each strip to get a larger total per cent of area in 
obtaining the average. 

Age of timber increases both the range of sizes and the variation 
in density. Old timber is never as evenly distributed as a young stand, 
owing to the progressive losses from natural causes. Mixed forests, 
composed of several species, are more difficult to average than pure 
forests of a single or of two or three similar species. There is greater 
irregularity both in size and distribution in the mixed forest. The 
greatest irregularities for a given tract are caused by differences in 
topography and soil, or site conditions, which are reflected in the char- 
acter of the stand. In mountainous topography, the entire forest 
changes from bottom to lower slope and from lower slope to upper slope. 
In more level topography, the type changes as abruptly and completely 
on the basis of the moisture content of the soil from swamp to drained 
bottom, from drained bottom to dry upland. Any system of timber 
estimating must be planned to secure: 

1. The separation of areas which differ radically from each other, 
but which within themselves are fairly uniform. These areas conform 
with the types of forest cover. 

2. An arrangement of the strips such as to secure the greatest pos- 
sible accuracy in sampling, which is done by crossing these variations 
of density, type and form, at right angles with their longest dimen- 
sions of area, as far as possible (§§ 219 and 228) 

The degree of detail and cost of the work as reflected either in an 
increased per cent of area or number of strips or an increased per cent 
of trees tallied for dimensions, either diameter or height, will thus be 
increased in proportion as 

The size of the unit diminishes. 
The size of the timber increases. 



266 ESTIMATION OF STANDING TIMBER 

The variety of the timber increases. 

The topography is more mountainous or varied, resulting in a 

greater diversity of types. 
The number of products required increases. 

Finally the degree of accuracy required, other things being equal, 
will depend upon the stumpage value of the products to be estimated, 
as influenced, first, by the character of the timber itself, and second, 
by the unit price of the product. In the earlier days crude and inaccu- 
rate methods of timber estimating were justified by the low price 
per acre and per thousand feet at which stumpage changed hands. 
With record stumpage prices running up to S27 per thousand feet for 
white pine in state auctions in Minnesota, in 1920, a degree of accuracy 
is justified which would not be thought of by old-time timber cruisers. 



CHAPTER XX 
METHODS OF TIMBER ESTIMATING 

213. The Importance of Area Determination in Timber Estimating. 

Except in a few instances where every tree on a tract is separately 
measured, all methods of timber estimating depend upon the principle 
of applying the results obtained on part of an area to the entire area, 
or on small portions of an area to larger subdivisions. Any error in 
determining the total area included within the boundaries of a tract, 
or the correct area of any subdivision made within it, will incur a cor- 
responding error in applying the results of the estimated portion to the 
whole. The separation of timbered from non-timbered areas is an 
example. If the average stand of the timbered portion is correctly 
found, but its area is estimated to be 10 per cent greater than it actually 
is, an error of plus 10 per cent is incurred in the estimate. Correct 
determination of areas of the tract and its timbered subdivisions is 
the first consideration in the field work of timber estimating and counts 
for fully half in the total scale of accuracy. 

The first essential is to locate and determine definitely the boundaries 
of the area to be estimated. Where the tract lies in regions subdivided 
by a rectangular system of government surveys this is not ordinarily 
difficult. The area may be approximately located with sufficient 
exactness for the work. Even here it is necessary to identify the 
section corners and sometimes to re-run the lines if time permits. In 
other regions where the land surveys follow an irregular pattern, the 
identification of the corners and lines is best accomplished by the aid 
of some local resident who is familiar with these bounds. The retrac- 
ing and mapping of the boundaries of a property is an essential step 
in management, but its cost is not properly chargeable against the item 
of timber estimating alone. 

If methods are used by which 100 per cent of the timber is estimated, 
the total stand can be obtained independent of the actual area or shape 
of the tract provided only that all of the trees upon it are counted and 
their contents determined. When for a 100 per cent estimate is sub- 
stituted an estimate covering only a part of the tract, the cruiser requires 
a knowledge of its shape and size. In the rectangular system of surveys 
most of the subdivisions are square and the smallest unit commonly 

267 



268 METHODS OF TIMBER ESTIMATING 

used contains 40 acres. Even here fractional lots lying along the north 
and west boundaries of a township or adjoining meandered streams 
and lakes call for a plot which shows their dimensions. With these 
rectangular areas it is a simple matter to obtain a definite per cent of 
the total by running strips of a given width. 

On irregular tracts, a map showing the boundaries and area is 
required to enable the cruiser to determine, first, in what direction and 
relation to lay out his lines or strips, and second, to compute the exact 
per cent of the total. This desired per cent is approximated and the 
exact relation secured is determined after the lines are run. 

214. The Forest Survey as Distinguished from Timber Estimating. 
Timber estimating may be undertaken for the sole purpose of determin- 
ing the volume of timber on a tract, but as commonly carried out, this 
requires the running of numerous definitely located compass courses, 
gridironing the area, which gives an opportunity for the collection 
of a large amount of additional data required in its permanent manage- 
ment and in the logging of the area. The collection of this additional 
data, together with the timber estimate, constitute what is termed a 
fored survey. Even the crudest work of timber cruisers embraces 
some elements of a forest survey. The features of such a survey are: 

1. A map showing the topography of the area either by hachures 
or contours, giving streams and ridges and other important features 
which influence logging and management. 

2. A map showing the character of the forest cover, classified as to 

(a) Timber types, corresponding with divisions made in the 
stand in timber estimating and showing blank areas, such 
as ^yater, barren, cultivated or grass-land. 

(6) Divisions due to age of the timber such as burns, re-stocked 
or l)arren, reproduction or immature timber, older age 
classes. 

3. Soil maps, locating land of agricultural value and land fit only 
for forest purposes. 

Under timber estimating proper, the forest survey makes an inven- 
tory showing both the quantity and quality of timber by different 
products, grades and sizes as required for the purpose of valuing the 
tract as follows: 

1. Quantity or vohmie. 

(a) Separately by species, 

(6) Separately by units of merchantable volume, as board feet, 

poles, cords, 
(c) Separately by character, as live or dead timber, sound or 

cull, and giving the net volume after deductions for cull. 



TIMBER APPRAISAL 269 

2. A statement of amount and character of damage present due 
to rot and other defects such as shake, fire damage to standing timber, 
the presence of insect damage, windfall. 

3. The quality and sizes of the timber under the items; average 
diameters, average merchantable length in logs, form of bole as to 
straightness, taper and clearness and finally the grades present, classi- 
fied either as log grades or as grades of lumber. 

The third class of data is that needed for permanent forest manage- 
ment for the production of timber by growth. These data are fre- 
quently omitted or overlooked in a timber survey, first, by old cruisers 
who have not been trained to collect them; second, by foresters who 
have failed to formulate a definite plan for their proper collection in 
anticipation of the need for its use. These data fall under: 

1. Age classes in the merchantable timber, either by area (maps), 
or by size or diameter (stand tables of diameter classes), or both. 

2. Age classes in immature timber either by areas as mapped, by 
per cent of area occupied or by tree counts; the ages and sizes of these 
age classes, their condition, thrift and the chances of survival. 

In addition, a forest survey may include data on all other resources 
of the forest such as forage for grazing, while under timber it should 
determine the areas included within different site classes (§ 227). 
Forest surveys include all data of every kind necessary for the making 
of a working plan for the management of the area for permanent forest 
production. 

215. Timber Appraisal as Distinguished from Forest Survey. The 
forest survey as described above is the preliminary step in the appraisal 
of the value of timber stumpage. This appraisal constitutes a separate 
operation, although the survey and the appraisal are so closely bound 
together that the}^ are frequently performed by the same man. They 
must not be confused, however, for a timber appraisal is not a part of 
Forest Mensuration, but belongs under the separate subject, Forest 
Valuation (§5). It may begin where the timber survey leaves off, 
using the data acquired by this survey. Separate parties may conduct 
the timber survey and the timber appraisal with satisfactory results. 

A timber appraisal covers the following points: 

1. Logging conditions summarized for each logging unit, under 
topogiaphy, slopes, surface, rock, brush and character of bottom as 
affecting logging. Transportation possibilities, availability of streams 
for log driving, routes for roads, flume or railroads, methods best adapted 
for skidding and hauling the timber and the costs of these processes. 

2. Costs of forestry such as the per cent of the stand to leave for 
seed or second cut. the cost of brush disposal and other protective 
measures. 



270 METHODS OF TIMBER ESTIMATING 

3. Economic conditions, markets and prices for lumber. 

4. General appraisal, cost of milling, cost of logging, cost of trans- 
portation, profits requii-ed. 

5. Specific appraisal, the direct cost of logging the specific body 
of timber and the resultant stumpage value of this unit. 

A clear-cut distinction between the work of timber estimating and 
of timber appraisal will prevent the mistake so often made of burden- 
ing the timber estimating crew with the work of recording in great 
detail items of cover, surface, brush, etc., which instead should he sum- 
marized for an entire unit by the person who appraises the value of the 
timber and sizes up logging conditions. It is seldom that the two jobs 
can be effectively combined in the same party or individual. The 
work of timber estimating requires routine and concentration on the 
details of the job. The actual appraisal, even if the same party makes 
it, should follow rather than accompany the estimate and should be 
based first, upon the data on topography as shown by the map and 
second, upon the data on volumes as shown in the estimate. 

216. Forest Surveying as a Part of the Forest Survey. A forest 
survey as above outlined includes the work of forest surveying or the 
determination of the boundaries and area and the mapping of the topog- 
raphy of a forest tract. This subject is not a part of Forest Mensu- 
ration, but must be treated separately. Since the gridironing of the 
tract requires the measurement of distance and direction and the plotting 
of these lines will give the framework of a map, it follows that the work 
of making a topographic map which may employ the same general 
methods of examination for the area, can he advantageously combined 
with the work of timber estimating. Timber cruisers usually prepare 
a crude map showing the intersection of streams and the position of 
ridges and other topographic features of importance. The prepara- 
tion of a map based upon basal elevations and giving contours is a 
development of the timber survey introduced by foresters and adds 
greatly to the efficiency of the survey. By combining this map-making 
with the entirely separate operation of estimating, a crew of two men 
can complete both operations with a very slight increase in expense, 
not comparable with the cost of doing each piece of work separately. 

At the same time the preparation of the type or timber-cover map 
can proceed, and upon this in many instances depends the accuracy 
of the timber estimate itself (§ 225).^ 

1 The detailed methods of Forest Surveying employed in a forest survey cannot 
be discussed in a text on Forest Mensuration without exceeding the limits of the 
volume. Any summary of a system of forest survey must include a description 
of the methods of surveying and topographic mapping which are to be used. The 
various methods of survey must be co-ordinated with the methods of cruising and 
with the cost and relative accuracy of the work desired, both for the survey and 
the estimate. 



THE CULL FACTOR, OR DEDUCTIONS FOR DEFECTS 271 

217. The Cull Factor, or Deductions for Defects. Most timber 
estimating for board-foot contents of stands is based on the amount 
which the logs will scale (§ 116). Since a sound scale of logs requires 
deductions for defects which will not make sound boards, the timber 
estimator must make the same deductions in the standing trees. This 
deduction from total sound scale is independent of any separation 
of the timber into grades or quality, which calls for additional special 
attention. Deductions from full sound scale of standing timber are 
made either by the log unit or by the tree unit on the basis of the judg- 
ment and experience of the cruiser. Where the estimate is made by 
logs, only sound logs are tallied. Culled logs are dropped from the 
tally altogether and trees which contain defective portions are scaled 
by shortening the length or decreasing the size of the logs tallied so 
as to represent only their net sound volume. Where it is impossible 
or inaccurate to use this method of omission, a straight percentage 
deduction for cull is either substituted for the method of dropping 
or reducing logs or is subtracted after all of the clearly visible defect 
has been deducted. 

Tree units are handled in the same manner. Trees so defective 
that they are practically cull are not tallied at all, but in species where 
few, if any, trees are cull and the defect constitutes a portion of a large 
per cent of the logs and is not easily deducted, cruisers deduct a straight 
per cent from the total sound scale of the trees tallied. Usually a com- 
bination of these methods is necessary since the per cent deducted 
represents more accurately the loss in the sound scale of logs actually 
sawed and taken to the mill, while a considerable additional cull is 
found in logs and trees not utilized at all. 

Foresters, in making a tally of diameters and heights, customarily 
tally all trees, regardless of their condition, omitting only dead timber 
which is unmerchantable, and then apply to the total volume a per- 
centage deduction for total cull, which will cover both that portion 
left in the woods and that lost in sawing. 

218. Total, or 100 Per Cent Estimates. To completely cover a 
small area, it is only necessary to avoid duplicating the count or measure- 
ment of the individual trees. This may be done by the use of a bark 
blazer or scratcher, or by tagging the trees, a method employed in India 
where labor is cheap. 

Trees may be given a light bark blaze. In working over a tract 
in this manner, the blaze is placed upon the same side of all trees, facing 
the direction towards which the measurement is proceeding. Where 
topographic features are present on small areas, duplication may be 
avoided by covering sections bounded by these natural features without 
the necessity of spotting the trees. 



272 METHODS OF TIMBER ESTIMATING 

On larger areas, where it would be impossible to keep track of the 
individual trees, parallel strips may be run. The trees on the outer 
edge of a strip 'can be blazed facing the strip which has not yet been 
measured, and in this way the entire tract covered with a minimum 
of effort. In dense swamps men may be employed to hew parallel 
lanes through the underbrush; the cruiser then estimates all trees 
between these lanes. 

It is possible to dispense with all methods of marking the trees 
provided sufficient care is taken, first, in running the strips accurately 
as to direction so that they lie parallel and at fixed distances apart, 
and second, by estimating or measuring the trees on strips so placed 
that they cover the entu'e area; i.e., strips whose borders are contiguous. 
There is danger of overlapping or duplication by this method, and if 
it is the intention to run a 100 per cent estimate, a slightly greater 
accuracy can be insured by blazing. This ocular method, however, 
is commonly employed as a substitute for blazing. 

A modification of this method of completely covering the area by 
strips, is the laying out of rectangular plots whose dimensions are such 
as to cover the area without overlapping. These plots are estimated 
consecutively and may be of any convenient width and length. As 
an example, a method given in Graves' Mensuration, page 196, consists 
in laying out two tiers of plots, each 40 rods wide and 16 rods across. 
Ten of these plots give the area of 40 acres. The cruiser proceeds 20 
rods from the corner of the forty, and then crosses the center of the 
first tier of five plots, returning through the center of the second tier. 

To get the contents of the trees on areas 100 per cent of which is 
estimated, the following systems may be used : 

1. Tally the merchantable contents of each tree directly. This 
is estimated by eye, or from a universal volume table which may be 
printed on a Biltmore stick, or any other convenient form. 

2. Tally the upper diameter, inside bark, of eiich log in the tree, 
or tally the upper diameter of the butt log and top log (see Rule of 
Thumb by F. R. Mason, § 204). The contents are then computed 
from a log rule. 

3. Tally the diameter and merchantable height in 16- or 32-foot 
logs or half -logs of every tree. The contents are then computed from 
a volume table based on similar dimensions. 

4. Tally the diameter only, of every tree, either by eye or by the 
use of calipers. Measure, by a hypsometer, several sample trees of 
each diameter to give a curve of average height on diameter. The 
contents of the trees are then computed from a volume table based 
on diameter and height. The heights measured maj^ be either merchant- 
able or total, but are usually the latter. In this method, types or areas 



ESTIMATES COVERING PART OF TOTAL AREA 273 

which differ in average height and diameter must be estimated sepa- 
rately. 

5. Count all the trees on the area and tally a fixed percentage such 
as 1 in either 3, 4 or 5, whose volumes are found as by method 4 above. 

6. Count all the trees on the area and determine their volume by 
arriving at the contents of an average tree. This may be done: 

By guessing at the average contents. 

By selecting a tree of average diameter and height and determin- 
ing its contents by the use of volume table. 

By determining the number of logs per tree or average mer- 
chantable height expressed in logs, thus getting the total 
number of logs on the area and then guessing at the con- 
tents of the average log or number of logs per thousand. 

Method 6 may be applied to all of the timber considered as one 
class, or the timber may be separated into two or possibly three dif- 
ferent classes, corresponding with marked differences in size and char- 
acter. 

219. Estimates Covering a Part of the Total Area. The Strip 
Method. There are two methods generally employed to estimate a 
portion of the area, the strip method and the plot method. The strip 
method adopts the principle of endeavoring to obtain the average 
stand per acre for the whole area, from the portion estimated by the 
running of strips parallel or in a given direction and spaced at mechanic- 
ally regular intervals. By this means it is sought to eliminate judg- 
ment or choice in the obtaining of the required average. 

This average is still further improved by the choice of direction of 
running these strips. The effect of differences in elevation and in drain- 
age or soil moisture is to produce differences in the density and character 
of the forest corresponding with these changes. The belts of forest 
which have comparatively uniform stands usually run parallel with 
contour lines and at right angles to the direction of slope. A basic 
principle of strip estimating is therefore to cross these belts at right 
angles or proceed directly up and down slopes or directly across the 
larger stream or drainage bottoms as far as possible, and to avoid 
traveling along contour lines or bottoms and in general along the long 
axis of belts of timber. If this fundamental principle is neglected, 
very large errors may be incurred in applying the average estimate 
so obtained to the larger area. 

In rectangular surveys, it is customary to run the strips in one of 
two cardinal directions, and the choice is therefore narrowed down to 
either north and south, or east and west. In irregular surveys, or 
where the topography is so mountainous that the estimate will be made 



274 



METHODS OF TIMBER ESTIMATING 



by topographic blocks and units, rather than by forties or legal sub- 
divisions, the system of strips will be planned with reference to base 
lines run along the main bottoms and streams, from which, at regular 
intervals, the strips will be run directly up the slopes and as nearly 
parallel to each other as possible. The strips in each separate unit 
may, therefore, have a different direction. 

220. Factors Determining the Width of Strips. The standard widths 
of strips used in timber estimating are six in number and their dimen- 
sions are given in the following table; 

TABLE XLI 
Relation of Width and Number of Strips to Area Covered 



Width of Strips 


Area covered by 

one strip per forty 

acres or four per 

mile. 

Per cent 


Strips per \ mile 
to cover entire 


Feet 


Rods 


Chains 


area. 
Number 


33 
66 
110 
132 
165 
330 


2 

4 

61 

8 
10 
20 


1 

2 
1 

2 

2^ 

5 


91 

5 

8§ 
10 
12i 
25 


40 
20 
12 
10 

8 
4 



On rectangular siu'vej'S, to compute this per cent of total area 
covered by the strips, multiply the number of strips run per forty 
or one-fourth mile square, by the width of the strip in rods, and divide 
by 80 rods. These two factors, number and width of strips, are not 
reciprocals since each has a distinct function to perform. The number 
of strips per forty increases directly the probability of accuracy 
in securing an average stand or proper sampling of the timber on the 
area (§ 211). The width of the strip affects this average to a lesser 
degree. Its principal function is to enable the cruiser to determine 
accurately the dimensions and volume of the trees which stand upon 
the strip estimated, and the factors which affect his ability to obtain 
this accuracy will determine the width of strip without respect to its 
effect upon the total area covered. If narrow strips must be run in 
order to get accurate estimates of timber on the strip, and it is necessary 
to increase the per cent of area, the number of strips will have to be 
increased rather than the width of the strip. 

An example of the relations between these two factors is cited by Austin Cary, 
Manual for Northern Woodsmen, where a system on the Pacific Coast of using two 



FACTORS DETERMINING WIDTH OF STRIPS 275 

strips per forty, each 10 rods wide, covering 25 per cent of the area was abandoned 
in favor of the use of a narrower strip 6f rods wide to increase the accuracy of the 
estimate on the strip. The nuinber of strips was then doubled, or four strips run 
per forty, and the total per cent of the area estimated was thus increased from 
25 per cent to 33| per cent. If, instead, the number of strips had been kept the 
same, but the width of each strip increased to 20 rods, a lesser degree of accuracy 
would have been attained in spite of an increase to 50 per cent of the area covered. 

In determining the number of strips required for a forest survey, 
the character of the topographic map desired must be considered with 
reference to the topography. Lines run ^-mile apart will give only a 
rough scale map in bold mountainous topography. Lines placed at 
j-mile intervals in mountainous slopes with large features, are sufficient 
for an accurate topographic map with a large contour interval of from 
50 to 100 feet. On all flat or gently rolling forested slopes with no 
outlook, cut up by drainage or interspersed with swamps, it is impos- 
sible to make an accurate topographic map with proper contour interval 
of from 10 to 20 feet and show all details of drainage and slope, unless 
lines are run at |-mile intervals, but this interval is sufficient for all 
maps on the ordinary scale of from 2 to 4 inches per mile. Only for 
a much greater detail will lines be required at less than this interval. 

The influence of the forest cover upon the number of strips required 
for accuracy increases with the two factors, density of the forest cover 
and variation of the timber, whether caused either by age, size or diver- 
sity of species. Finally, the increasing value of the timber from any 
cause, whether through quality or unit price, will require an increase 
in the per cent of area covered, which means a greater number and 
more closely spaced strips. 

These conditions frequently require a full or 100 per cent estimate 
by forties, the best examples of which are the heavy stands of rapidly 
increasing value in the Pacific Coast States, or stands of large mature 
hardwoods with great variety in size and value. 

The width of strips is determined by the accuracy with which this 
width can be measured by the eye and the dimensions of all the trees 
standing thereon ascertained, or the timber upon it measured and 
counted. This width is diminished directly by the amount of brush 
and undergrowth which obstructs the vision. In brushy country, strips 
seldom exceed from 4 to 6f rods. The width of a strip is also diminished 
by decreasing size and increasing number of trees on the strip. In 
young timber, with many stems per acre, a greater degree of accuracy 
is obtained on a 4-rod strip accurately measured and counted than 
upon a strip of twice the width. Conversely, open and large timber 
with fewer and more scattered trees and an unobstructed view not 
only permits a wider strip to be measured accurately, but requires an 



276 METHODS OF TIMBER ESTIMATING 

increase in the per cent of area, which is easily obtained by increasing 
the width of the strip without an appreciable increase in the cost. This 
is independent of the need for running more strips per acre, by which 
the per cent is still further increased. With unobstructed vision, a 
wide strip may be estimated with almost as great accuracy as a narrow 
strip, since the error may be in proportion to the total width without 
affecting the percentage of error in the estimate. 

With increasing openness and irregularity of timber, strips may 
give way altogether to a total count of timber on an entire forty, 
since no system of partial or sample estimates can be depended upon to 
secure an average oi- a correct total. 

The method of determining the volume of the trees on the strip 
affects the width of strip which can be used accurately. Where trees 
are counted, without measuring the diameter of each tree, nearly 
double the width of strip can be used because trees can be seen for 
this additional distance while it is less possible to judge their diameters 
accurately. Upon a calipered strip, the additional width sometimes 
slows up the work and introduces a greater per cent of error. 

The counting of trees in open country is so simple a matter that 
cruisers accustomed to estimating such species as longleaf pine in the 
South have usually abandoned the strip method altogether. Guided 
by the compassman, they cross a forty about twice, pursuing a 
snake's course back and forth, and attempting to see and roughly to 
count all of the trees on the forty. 

221. Method of Rumiing Strip Surveys. Record of Timber. 
Strips are universally run with the compass. A hand compass is com- 
monly used by cruisers working in dense, swampy or brushy country, 
as it is more quickly read and increases the number of sights possible 
without delaying the work. For ordinary accurate surveying, in which 
a topographic map is made, the use of a staff compass adds to the accu- 
racy of the direction of the strips, and is commonly employed (Fig. 
58). In the use of either hand or staff compasses, it is a great advan- 
tage to be able to turn off the declination of the needle on a movable 
arc with a vernier so that a cardinal direction is indicated by the sights. 
This is especially true in the Pacific Northwest, where variations up to 
25 degrees are encountered. 

The size of the field party for strip estimating depends upon the 
methods used in measuring and recording the timber. Wliere the 
diameters of each tree are measured either with the calipers or Bilt- 
more stick, the party will consist of three or four men to best advantage. 
One man runs the compass and makes the topographic and type maps. 
A second man tallies the diameters; the third and fourth work, one 
on each side, calipering trees. Heights are usually taken at regular 



METHOD OF RUNNING STRIP SURVEYS 



277 



intervals so as to be distributed uniformly over the area. Consider- 
able errors may be incurred in bunching sample heights in timber which 
may be too tall or too short 
for the average of the stand. 

Where diameters and mer- 
chantable heights are meas- 
ured by the eye, the party is 
usually reduced to two men, 
one for the compass and map, 
the other to record the dimen- 
sions of the trees which he 
estimates. It was a common 
practice in the Lake States 
in earlier days, for timber 
cruisers to work alone without 
the assistance of a compass- 
man. The system of counting 
timber and recording merely 
the average dimensions and 
volume enabled a man to run 
his own compass, keep track 
of his paces, and at the same 
time count the trees. 

The record kept by cruis- 
ers on strip estimating con- 
sists primarily of a tally of 

the trees by diameter, height, or volumes direct; second, of the 
cull, per cent; third, notes on damage to the stand; fourth, 
quality of timber and grades; fifth, young timber and reproduction; 
sixth, soil and ground cover. A report or summary sheet for each sepa- 
rate unit, usually by forties, is worked out. The following headings 
are submitted as samples (p. 278) : 

In the Appalachian region upwards of twenty species and a variety of products 
may be estimated. For the hardwoods, volume tables based upon diameter and 
merchantable log lengths are used. It has been found necessary to have available 
a table for one- and two-log trees to avoid errors in inaccurately applying small top 
diameters for these trees rather than the actual merchantable top. Cull is deducted 
from each tree by reducing the D.B.H. or number of logs. An additional per cent 
is deducted for unseen defects. The tally is coordinated with existing volume 
tables to secure a record of lumber, cordwood (principally acid wood), poles, ties, 
posts, or other products. An example of the tally form used is shown on p. 279. 




Fig. 58. — Staff compass. 



278 



METHODS OF TIMBER ESTIMATING 



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METHOD OF RUNNING STRIP SURVEYS 



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280 METHODS OF TIMBER ESTIMATING 

REVERSE SIDE OF BLANK 

Forest types, Lower slope 

Age classes, 1-60 

Condition of timber, Immature 

Thrifty 95 per cent 

Mature 2 per cent 

Decadent 3 per cent 

Fire killed per cent; damaged, 5 per cent 

Insect killed per cent; damaged, - per cent 

Other killed per cent; damaged, 2 per cent 

Name of disease. Bark disease 

Species affected. Chestnut 

Quality of timber {give by log grade; percentage of tall, medium or short clear boles; 
or number of clear logs of stated minimum length and diameter) : 

80% tall; 15% medium; 5% short 

Logging factors: 

Undergrowth; light-medium-dense. Light 

Windfall; light-medium-dense. None 

Bowlders and broken rock; numerous; occasional; absent. Absent 

Other factors, Easy gradient. Logging conditions ideal as skid and wagon 
roads can be constructed anywhere 

Replacement: Species ■ Per cent 

No replacement, 

Ground one-third stocked, 

Ground two-thirds stocked, 

Ground fully stocked. Chestnut, 50%; white, 5%, red, 5%, 
black, 20%, and chestnut oaks, 10%; white, 1%, 
pitch, 2%, and scrub pines, 2%; gum, 2%; sourwood, 
1%, and maple, 2% 100% 

The stand shows an absence of poplar due to grazing 

Additional Notes: This is a stand which was cut over for charcoal during the war 
and since then was culled for chestnut ties and poles. Bark infested chestnuts 
should be cut as well as suppressed chestnut for extractwood. The few mature 
"wolf" trees left from former cuttings should be removed as well as some of 
the scarlet and black oaks where the stand is too dense. Removal of the 
latter can be made for ties. The dead and down timber from the laps in the 
tie and pole cuttings should be removed for extractwood 



TYING IN THE STRIPS. THE BASE LINE 281 

Explanation of Blank, by Supervisor J. H.Fahrenbach. 

All saw timber is tallied by the number of 16-foot logs in each tree. If a tree 
happens to have odd lengths " we give and take." 

Under chestnut all trees to be removed for extract wood are tallied in the " " 
column. All trees to be left are tallied in the one-log column, even though they 
are not large enough to make one 16-foot log as is the case in trees imder 10 inches 
D.B.H. Street railway ties (6 by 6 inches by 8 feet) are taUied in trees which 
have reached their maximum value for hewn ties. Standard gage ties are usually 
sawed in saw timber operations, and are tallied as saw timber. Poles are tallied 
by diameter class. In this way we are able to approximate the number of 25-foot, 
30-foot, 35-foot, etc., poles. 

Chestnut oak and hemlock trees, suitable for bark alone, are tallied in the " " 
column. In figuring the estimate for bark the number of trees tallied as saw timber 
must also be included. It sometimes happens that we also have a market for black 
oak bark, and in this event a " " column must be entered under mixed oak. 

Poplar and scrub pine pulp wood are entered in the "0 " column. 

We class black, scarlet, pin and Spanish oak under mixed oak. If a " " column 
is added, it is understood that black-oak bark is to be entered. Under mixed-oak 
ties red-oak ties are included. 

Pitch, short-leaf and table-mountain pine are tallied under yellow pine. 

If there is a market for locust-tree nails they are tallied in the one- and two-log 
columns for the larger locust trees and the smaller trees are tallied as posts, using 
as a basis a post 4 inches in diameter and 7 5 feet long. 

Under others are tallied beech, birch, gum, maple, sourwood and sycamore. 

If there should be other valuable species for which provision has not been made 
in the headings the diameter and number of logs in each tree are given at the bottom 
of the Form. This includes walnut, ash and wild cherry. 

If there is a market for fuel wood, provision must be made for a " " column for 
all those species which cannot be utilized for either bark, pulp or extract wood. 
All the oaks can be thrown together in one heading, the pine in one heading and the 
remainder of the species, except hickory, in another heading. 

222. Tying in the Strips. The Base Line. In laying out and 
recording the strips run in estimating, independent of the question 
of topographic mapping, it is necessary to tie in each strip to a known 
point at each end, so that its position and the error incurred in running 
it in both distance and direction may be determined. For this 
purpose, and also to form the basis of a map when one is constructed, 
a base line is first surveyed along the route from which the strip will 
be later laid out. The strip, whether rectangular or irregular areas 
are being estimated, will start as nearly at right angles as possible from 
points on this base line, and will either be tied in to a second base line 
approximately parallel to the first, or by offsets will be run back at the 
proper interval and tied in to the original base line. 

In laying out this base line, therefore, stations or measurements 
are established at the exact points and intervals from which these strips 
must later be initiated and tied in. Methods of survey and establish- 
ment of base lines fall under the subject of Forest Surveying. The 



282 METHODS OF TIMBER ESTIMATING 

base line is a primary feature of the forest survey. Where a land survey 
exists which is accurate and easily traced, or where such a survey is 
retraced, it may serve as a base line. 

Where the area is small, and a survey and map exists, the corners 
and known or located points on the boundaries of the tract are sub- 
stituted for a base line as points from which to initiate strip surveys. 
The same rules apply as to the necessity of tying in each strip on its 
completion to some known point on the map, in order to check errors 
in the survey which would affect the areas determined. 

In running the strip, the estimator is dependent upon the compass- 
man for the distances from which the areas are determined and the 
estimate separated by 40-acre tracts. Errors in measuring this dis- 
tance will cause the cruiser to misplace timber, thus altering the accuracy 
of the individual estimates per forty. Where types or differences in 
stand are separated in estimating, the distance across each separate 
type, as kept by the compassman, will determine the area and con- 
sequently the accuracy of the estimate within the type. If errors are 
incurred, their character and extent is revealed by tying in to known 
points, which enables the construction of a correct map and the correc- 
tion of the estimates. 

In running estimates over separate forties, it is customary to run 
strips 1 mile in length, cruising a tier of 4 forties before returning. 
Where one strip per forty is run, the estimate for the forty is completed 
at the end of 80 rods. Where two or more strips are run per forty, 
the tally of the timber on each forty is separated for each strip as indi- 
cated to the cruiser by the compassman, and is not completed until 
the last strip on each forty is run. The results for each strip on the 
same forty are usually tallied together on the same sheet, and care 
must be exercised not to misplace or mix up these tallies. 

223. Systems of Strip Estimating in Use. Examples of systems of 
estimating in which the various factors itemized above are harmonized 
to meet a given set of conditions, are given below: 

Forest Service Standard Valuation Survey. This system was used almost uni- 
versally by the Forest Service and with minor modifications is still a standard method 
used on national forests. Its characteristics are: 

Width of strip 4 rods or 1 chain 

Number of strips per forty 1 to 2 

Per cent of area estimated 5 to 10 

Measurement of distances By chain or tape 

Measurement of trees, diameters By calipers or Biltmore stick or ocular 

Heights Sample heights by hypsometer 

Forest types Separated and coordinated with aveiaj^c- 

heights 

Cull factor Estimated by a total per cent 

Corrections from strip estimate for 
average stand None 



SYSTEMS OF STRIP ESTIMATING IN USE 283 

In this system, as indicated in the last item, no effort was made to modify the 
average stand per acre obtained from the strip in order to get a more correct total for 
the area. The employment of inexperienced men made necessary the use of instru- 
ments for diameter and height measurement, and the rigid elimination of the element 
of judgment on every point possible. Where the unit of area was large, from 1 
square mile up, this method gave excellent results, since the mechanical average for 
areas of this size is quite dependable on the basis of a 5 to 10 per cent estimate. 
The errors possible could be easily avoided by conscientious effort. These errors 
consisted of too wide or narrow a strip, diameters measured too low, average heights 
measured too high, dead trees calipered for live ones. When applied to large timber 
in units of 40 acres or less, these mechanical results cannot be depended upon. 

Lake States Cruisers' Method 

Width of strip 8 to 10 rods — 2 to 2^ chains 

Number of strips per forty ... 1 to 2 

Per cent of area estimated 10 to 25 

Measurement of distances By pacing 

Measurement of trees Counted 

Heights Average number of 16-foot logs per tree 

Volume From number of logs on tract and log run, or 

contents of average log 

Forest types Timber of different age classes and quality 

separated 

Cull factor Usually by per cent deduction from total esti- 
mate 

Corrections from strip estimate for 
average stand Close inspection of remaining area and modifi- 
cation of average whenever necessary to 
obtain correct total 

Of late, timber cruisers in these states have been adopting the use of volume 
tables, but in many instances these tables are based upon stump diameter inside 
the bark which makes them less consistent and accurate than if based on D.B.H. 
The more modern cruisers are adopting the use of standard volume tables constructed 
by regular methods and differentiated by D.B.H. and height. 

Southern Timber Cruisers' Methods 

Width of strip A strong tendency to substitute ocular esti- 
mate, based on the stand per acre, for the 
running of strips. Great carelessness in 
methods until recently 

Measurement of distances Paced by a compassman, the cruiser usually 

riding a horse. Consequently estimates fre- 
quently stopped at the edges of swamps 

Measurement of trees Cruiser gets located by compassman, but does 

not follow the strip. Trees are counted on 
acre plots 

Volume of average tree Guessed at, using rule of thumb based on 

Doyle rule. Trees on entire forty may be 
counted to check results of plots and get 
reduction factor 



284 METHODS OF TIMBER ESTIMATING 

Forest types Accuracy of the better class of cruisers greatly 

increased by careful elimination of blank 
areas and containing net area of timber to 
which reduction factor from stand per acre 
is applied for total 

Cull factor Usually neglected on account of deficiencies in 

Doyle scale 

Corrections from strip estimate for 

average stand This is based on general inspection and count- 
ing since no. systematic strips are run 

Many Southern cruisers have adopted more systematic methods of late. 

Yale Forest School Method in Southern Pine. 

Width of strip 10 rods — 2^ chains 

Number of strips per forty 2 

Per cent of area estimated 25 

Measurement of distances By pacing 

Measurement of trees Count of the trees on the strip, tally of one- 
third to one-fifth of the timber by mechan- 
ical selection to avoid choice. 

Diameters Tallied by eye 

Merchantable height Tallied by eye in 16-foot logs and half-logs of 

all trees whose diameters are tallied 

Volume on strip From volume table for trees tallied multiplied 

by 3, 4 or 5, according to per cent tallied 

Forest tyjjes Areas not stocked with merchantable timber 

eliminated by mapping. Net area of timber 
obtained. Types not usually separate 
within a forty except on the map 

Cull factor By per cent of total estimate 

Correction from strip estimate for aver- 
age stand Careful inspection at stated intervals of stand 

on remainder of forty. Comparison by 
weighted volumes with stand estimated. 
Weighted correction factor applied to area 
estimated to obtain proper stand per 
forty 

Horseshoe Method. This is a modification of the strip method, by which two 
strips are practically combined in one by running a horseshoe or angular course 
through the forty as shown in Fig. 59. This results, first, in a saving of time, cut- 
ting down a certain amount of travel from one strip to another; second, in a better 
inspection of the timber and, it is thought, in a better average, since the strips run 
in both cardinal directions. This method was employed extensively by a firm of 
Southern timber cruisers, who used a 10-rod strip, thus running 25 per cent of the 
area. 

Pacific Coast Method. 

Width of strip 10 rods, or 2| chains 

Number of strips per forty 4 

Per cent of area estimated 50 

Measurement of distances By pacing 



METHODS DEPENDENT ON THE USE OF PLOTS 



285 



Measurement of trees The volume of each tree recorded directly, 

based upon the universal volume tables 

Forest types Not necessary to regard them 

Cull factor Deductions made for each tree when its 

volume is ascertained 

Correction from strip estimate for aver- 
age stand By running 50 per cent, corrections are usually 

avoided. Where inspection reveals the 
necessity, modifications are made in the 
total estimate 

Separate record under this system may be made of the board-foot 
contents and of other products, such as poles. The estimate is fre- 
quently increased 
to 100 per cent. 

These examples 
are cited merely to 
show the various 
combinations of ele- 
ments which go to 
make up a system 
of timber estimat- 
ing. The securing 
of accuracy consists •- 
in adapting the Fig 
number and width 
of strips to the 

local conditions described as, first, character of timber 
estimated and, second, size of the smallest unit of area 
estimated. The details of measurement, whether by eye or 

















r 




"H 






r 




"1 


















1 
1 
1 

1 
1 




1 


l_ 






_j 


L 

























1^ 



Mile 



59. 



Horseshoe method of strip estimating. Route 
of compassman shown by dotted line. 



to be 
to be 
instru- 
ment, for distance or for tree dimensions, must be coordinated with 
the volume table and with the skill and personal ability of the individ- 
uals employed in the work. The saving in time by the substitution 
of the eye and of ocular judgment requires dependence upon personal 
skill. Where cruisers with sufficient experience are unobtainable, 
accurate results may still be obtained by mechanical measurements, 
carefully supervised and conscientiously applied. 

224. Methods Dependent on the Use of Plots Systematically 
Spaced. In the use of plots in timber estimating, the method employed 
depends upon whether the principle of mechanical arrangement or 
spacing is to be observed, in order to obtain an average stand, free 
from the element of personal judgment, or whether instead, plots are 
to be selected by the use of judgment in an effort to obtain thereby 
an average stand which will apply to the area as a whole. By the 
first principle, the plot method, so-called, is merely a modification of 



286 



METHODS OF TIMBER ESTIMATING 



the strip method. Compass strips are run at the usual intervals, 
but instead of a continuous belt or ribbon of area being covered, this is 
broken or separated into plots at fixed or stated intervals along the line. 

These plots may be rectangular, but the use of such plots is not 
common. In the measurement of rectangular plots, a crew is usually- 
employed, and this same crew can probably run out the entire strip 
with better results. Rectangular plots for the measurement of young 
growth and reproduction, which is desired only on a small per cent 
of the area, are frequently used in conjunction with a strip for the 
merchantable timber. 

The common form of plots is circular to enable one man to work 
to advantage without the assistance of a compassman. By dividing 
the functions of pacing and compass work from those of estimating 
and recording the diameters and heights of timber, the mind is kept 
free for concentration on each task in turn. A crew of two men is 
sometimes used for circular plot estimating with the same advantage 
to the timber cruiser, who can inspect the stand for defect and quality 
between the estimation of the volumes of his plots. The common 
size of plots is as follows : 

TABLE XLII 
Sizes of Circular Plots 



Size of 
plot. 

Acres 


Radius. 

Feet 


Diameter 


Feet 


Rods 


1 

4 
1 

2 

1 


59 

83 

118 


118 
166 
236 


7.15 
10.0 
14.3 



The relation of these plots to the per cent of area covered is given 

below. 

TABLE XLIII 
Relation between Plots and Area Covered 



Size of plot. 


Shortest 
distance 
between 
centers. 

Rods 


Plots for i 

mile of 

strip 


Total area 

included in 

plots. 

Acres 


Per Cent of 40 Acres 
Included in Running 


Acres 


1 strip 


2 strips 


1 

4 
h 

1 


8 
10 
16 


10 

8 
5 


21 

4 

5 


6i 
10 

m 


12^ 

20 

25 



METHODS DEPENDENT ON THE USE OF PLOTS 287 

Great care must be taken in the use of circular plots to obtain the 
width of the plot correctly. An error in this factor is more serious than 
that on a strip, since it affects the entire boundary. The same principle 
as to size and number of plots and per cent of area covered applies 
to these methods as to strip estimating. In dense brush and with small 
timber, the common size is one-fourth acre, while plots 1 acre in size 
are required for old and large trees. The amount of timber on each 
plot is obtained by the use of the same variety of methods as for strips. 

Examples. Spruce in the Northeast on large tracts. 

Size of plot J acre 

Number of strips per forty 1 

Distance between plots on strip 20 rods — 5 chains 

Per cent of area covered 2§ 

Measurement of distances By pacing 

Measurement of trees D.B.H., cahpered or tallied by eye 

Heights A few sample heights taken on each plot for 

curve of height on diameter 

Types Separated in mapping 

Cull By per cent applied to total estimate 

Correction of estimates to get average . None 

Large Timber on the Pacific Coast. 

Number of strips per forty 1 to 2 

Size of plots 1 acre 

Number of plots per strip 5 

Per cent of area 12^ to 25 

Measurement of distance By pacing 

Measurement of trees on plot Average tree selected for each species. Diam- 
eter at stump inside bark and at top 
measured. Average of these diameters 
taken as diameter of the average log 

Volume Obtained by rule of thumb (§ 214). (Any 

of the three standard methods for obtaining 
the contents of trees on a plot or area apply 
to this method.) 

Tj^es Blank areas eUminated and stand obtained for 

average acre 

Cull By a per cent of the total estimate 

Correction factor to the estimate Obtained by general observation and com- 
parison with stands on the plots 



CHAPTER XXI 

METHODS OF IMPROVING THE ACCURACY OF TIMBER 

ESTIMATES 

225. The Use of Forest Types in Estimating. When only a part 
of the area of a tract is covered in estimating, the accuracy of the 
resultant estimate depends upon the success with which the actual 
average stand per acre has been obtained. Although the per cent of 
area taken has been properly chosen to fit the topographic conditions 
and character of the timber and although the measurement of the timber 
upon this area and the width of the strips has been accurately carried 
out, so that no avoidable error remains in the work done, yet the esti- 
mate may still be in error by the failure to secure the same proportion 
of the different types and variations of stand on the strips as exist on 
the area as a whole. On account of the prohibitive expense of running 
a sufficient per cent of the area to get this average mechanically, a 
margin of error in timber estimating is permitted, and is gaged by the 
value of the timber and the purpose of the estimate. Any modification 
which will secure the required degree of accuracy and at the same time 
avoid incurring an unreasonable expense will necessarily become a 
part of the system employed. 

The more uniform the stand as to sizes and density of stocking, the 
better the averages. This applies to the use of all six of the classes of 
averages cited in § 209. 

For the purpose of securing a greater degree of uniformity in the 
stand on those subdivisions of total area to which the estimates obtained 
on strips or plots are applied, the distinction of forest cover types is 
indispensable. A forest type includes all stands of similar character 
as regards composition and development due to given physical and 
biological factors, by which they may be differentiated from other 
groups of stands. A cover type is the forest type now occupying the 
ground, whether this be temporary or permanent. Timber estimating 
concerns itself only with the existing forest cover. 

The factors which are reduced to greater uniformity by the sepa- 
ration of forest types in estimating are composition of stand as to species, 
and consequent relative per cent of total volume of stand represented 
by the different species, a vital consideration in timber estimating. This 

288 



THE USE OF FOREST TYPES IN ESTIMATING 289 

factor has an influence upon the total vokime of the stand, as well as 
its average height, though both of these are influenced even more pro- 
foundly by differences in quality of site within the same cover type. 

These differences in type may be caused by altitude, slope, moist- 
ure and depth of soU. By separating the total into sub-areas, a far 
greater uniformity of size and density of the timber in these sub- 
divisions may be obtained, first by securing a more uniform mixture 
of species in the per cents of the different species represented in the 
stand ; second, by reducing differences in the density of stocking per 
acre; third, by securing more uniform sizes both in height and diameter, 
and* a smaller range. The subdivision of an area into a number of 
smaller units is a means of avoiding the necessity for securing a weighted 
average of these factors in order to get the average acre. Doubling the 
number of strips would probably secure the same result, but the expense 
of separation of the estimate into two or more types is much less than 
this increase in field work. 

The only increased expense of separating types consists of the 
increase in computations required by separating the areas and the 
precaution required in changing the tally sheet on entering the type. 
Proper coordination between the compassman who maps the area 
and the estimator who records the timber is necessary. 

Where areas as small as 40 acres are mapped and a large per cent 
taken, distinctions between the two types of timber are not often made 
by old woodsmen. The total volume of each species is obtained with- 
out separate computations of area. 

But the principle of type separations is universally applied in sepa- 
rating areas which do not contain merchantable timber from those which 
do. Blank areas caused by cultivation, burns, swamps, or uimierchant- 
able reproduction must be subtracted from the total timbered area 
under any system which permits the completion of a cover map. The 
arbitrary inclusion of these unstocked areas makes it practically impos- 
sible to obtain an average stand on the remainder. In theory the same 
law of averages applies even in this case and with a sufficient number 
of strips which cross blank areas in such a way that a per cent of the 
blanks is taken as the merchantable stand, no error would be incurred 
in the average. But the extreme danger of obtaining a different per 
cent from that on the whole tract, and the comparative simplicity 
of mapping out these blanks to obtain net timbered area, makes this 
method universal wherever the number of strips per forty or |-mile 
amounts to at least two, and possible even when but one strip is run. 
This correction requires, first, the area of the type whether timbered 
or blank, from a map; second, the area covered by the strip in esti- 
mating. The latter expressed in acres is computed by multiplying 



290 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 




Fig. 60. — Polar planimeter. 



length of strip by its width. The most convenient units are rods, 
since 160 square rods equals 1 acre, or chains, 10 square chains to 1 
acre. Distance in chains on strip required for 1 acre may be computed 
for each width of strip and the area of the strip obtained by dividing 
its length by this factor. 

226. Method of Separating Areas of Different Types. To determine 

the total area of 
the type accurately 
from a map, a 'plan- 
imeter may be used. 
By the use of 
this instrument a 
direct reading on 
the map is obtained 
in square inches 
of the area whose 
boundary is traced 
by the needle, moving clockwise. The stationary pin is placed outside 
of the area to.be traced. When placed within the area so that the 
movable pin finally encircles the pivot before returning to its point of 
origin, a deduction or correction must be made in the indicated area, the 
size of which depends upon the make of instrument used. 

The equivalent in acres for square inches, as determined by scale 
of the map, gives the acreage. Lacking a planimeter, the area of types 
can be computed by the method of approximation through triangles 
or the sum of small squares. For the latter purpose a map should be 
plotted on fine cross-section paper. 
The area of these types is required 
only to a reasonable degree of 
accuracy since the determination 
of their field boundaries is a 
matter of inspection and sketching 
and the total area of the tract is 
not involved. i 



Type 1 



n ---. 



Type II 



As an illustration of the effect of 
using type areas in estimating, the follow- 
ing example may be cited: Area of 
tract, 200 acres, divided into two types 
containing 100 acres each. The stand 
on the first type is 30,000 board feet per 
acre, and on the second 10,000 board feet. 
The total stand is therefore 4 million 

board feet. Twenty-five per cent of this area or 50 acres is to be covered by 
strips. The result of the cruise is shown in Fig. 61. 



Fig. 



61. — Relation of areas of types to 
strips in timber estimating. 



SITE CLASSES AND AVERAGE HEIGHTS OF TIMBER 291 

The result of running the five strips at regular intervals is to include within 
type I, 30 acres, which at 30,000 board feet per acre would give 900,000 board feet. 
In type II, 20 acres was included which at 10,000 board feet gives 200,000 board 
feet, a total for the 50 acres run, of 1,100,000 board feet. As this is 25 per cent of 
the area, the required factor for the tract without subdivision into types would 
be a multiple of 4, giving an estimate of 4,400,000 board feet, an error of +10 per 
cent caused not by errors in the strip but by failure to get the weighted average 
stand from the strips run. 

But if while running these same strips the tally sheet had been changed wherever 
the strip passed from one of these types to the other, and both the map of the area 
and the corresponding estimate of the timber, or tally, had thus been separated 
into two areas, corresponding with each of the two types, the computed estimate 
would show that while on 30 acres 900,000 board feet was tallied the average acre 
for type I is 30,000 board feet, but instead of this applying to three-fifths of the total 
area, it applies only to the actual area shown to be in the type, or one-half of the total, 
which is 100 acres, totaling 3,000,000 board feet. The less fully-stocked type in 
the same way is shown to contain 1,000,000 board feet or a correct total for the tract 
of 4,000,000 board feet. The 10 per cent error incurred in the first method is elimi- 
nated. The accuracy of this area correction obviously depends first upon ability 
to obtain by sketch a correct map of the actual areas of the different types, and 
second, to convert this area from the map into acres by use of the proper methods 
of map reading as explained in this paragraph. 

This system of type divisions is of especial value in mountainous regions where 
sharp distinctions can be drawn between types coinciding with great differences 
in the average density, volume, size and value of the timber. Under such circum- 
stances the more valuable types would require a greater per cent of the total area 
to be estimated, to obtain the same basis of accuracy as could be secured for the 
less densely stocked and less valuable tracts with a smaller per cent. The type ■ 
divisions also are more conveniently made in large or irregular areas than where 
estimates are separated by rectangular tracts of 40 acres. 

227. Site Classes and Average Heights of Timber, bifferences 
in the quality of the site on which timber is growing cause very great 
differences in total volume per acre, and in the total heights of the 
trees and stands. To quite an extent these differences are closely 
correlated with changes in cover types, different types being found 
on wet soils, fresh well-drained soils, and dry, shallow soils. But it 
often happens that the same type of forest cover will extend without 
appreciable changes in composition over a range of site quality so great 
that it becomes necessary to subdivide the area within the type into 
from two to three site classes, ranging from good to poor. This is 
made necessary by the effect of site upon the height of the trees in the 
stand, on account of the methods usually required, of selecting sample 
trees to measure for height. 

Heights constitute an extremely variable factor in timber estimating. 
Not only do total heights range through limits of at least 100 per cent 
for the same diameter, but merchantable heights, especially in old hard- 
woods, vary still more widely. Just as, in a 100 per cent estimate, 
the necessity for averages is eliminated, so when the height of every 



292 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 



tree in a stand is tallied there is no necessity for average heights. Only 
when merchantable log lengths are used as the basis for height will the 
height of every tree measured for diameter be tallied. Where total 
height is used, far greater accuracy can be obtained by the measure- 
ment of a few trees with a hypsometer than by attempting to guess 
by eye the height of each tree. 

In a large tract with varying site qualities, the securing of the average 
height for each diameter class from a range of heights of 100 per cent 
would require the selection of heights on the basis of the principle of 
a weighted average. If exactly the same proportion, as for instance, 
1 per cent, of the heights for each diameter were obtained from large, 
medium and short trees as existed in the original stand on the entire 
tract, the height curve could then be applied to the tract as a whole. 
Any failure to secure this weighted average would result in a curve 
giving too high or too low an average for the timber as a whole. 

The difficulty of securing a weighted average is eliminated if the 
tract can be divided into two or three site qualities, separated as dis- 
tinct units in the field in estimating. On each of these separate sites 
the heights conform to a much closer range for the same diameter than 
for the entire area, and a few selected trees for each class will give a 
dependable height curve (§ 209) from which the volumes in each 
diameter class may be acciu-ately computed. 

228. Methods of Estimating which Utilize Types and Site Classes ; 
Corrections for Area. An example of the application of these principles 
is found in the standard methods of timber cruising adopted by the 
Forest Service in the Appalachian region. Four types are used, termed 
cove, lower slope, upper slope and ridge. The variations in the per 
cent of estimate required are shown in the following table: 

TABLE XLIV 
Per Cent of Total Area Required in Estimating 





Total Area Estimated { 


Area 
of 














estimate 


Average 


Heavily 


Lightly 


unit. 


of all types. 


timbered 


timbered 






types. 


types. 


Acres. 


Per cent 


Per cent 


Per cent 


0- 100 


50-100 


50-100 


50 -100 


100- .500 


25- 50 


25-100 


10 - 25 


500-1000 


10- 15 


20- 50 


5-10 


1000-5000 


5- 10 


15- 25 


2i- 5 


5000 + 


3- 5 


10- 25 


i¥- 2§ 



THE USE OF CORRECTION FACTORS FOR VOLUME 



293 




The problem of combining a large per cent of area on a heavily 
timbered type, as the cove type, with a small per cent elsewhere, has 
been solved here by running strips across the entire area, embracing 
the minimmn per cent. Where these strips cross the cove types, points 
are marked on the ground which serve to tie in the strips run through 
the coves. Where 100 per cent is not estimated, a plan of running 
strips in a zigzag course from one boundary to the others of the type 
through these Qoves has been adopted. The more acute the angle 
between two courses and the 

more nearly parallel the result- ^^_^^.jn::^=^-'''^'^~'^'^'~T^' 
ant strips, the greater the per 
cent of the type included. 

229. The Use of Correction 
Factors for Volume. The pur- 
pose of all estimates is to secure 
the actual volume of timber on 
the entire tract as accurately 
and inexpensively as possible. 
In systems of covering partial 
areas, even after the probable 
error has been reduced by adopt- 
ing subdivisions based on type 
or forest cover and site, there 
remains a final possibility that 
the average stand per acre within 

the type differs from that secured by the methods employed.^ The older 
and more diversified a stand, the greater will be its irregularity of stocking, 
and the greater the necessity for accuracy. Can this accuracy be still 
further improved? A correction of an average, mechanically obtained, 
rests upon the assumption of definite knowledge that this average is 
wrong, and the ability to determine approximately how much it is in 
error. Since the timber on the area lying outside the measured and 
estimated strips is neither counted nor measured, the impression that 
the average is wrong depends upon the ability of the cruiser to estimate 
or size up timber by the eye and to compare it ocularly as a whole with 
the stand upon the strip which he has measured. This comparison 
is useless unless enough of the remaining timber can be seen so that 
it is practically certain that the average stand on the whole remaining 
area is greater or less than that measured on the strips. Where strips 
are narrow and run at wide intervals, it is impossible to arrive at this 
judgment and no reliable correction can be made by eye. 

1 Errors in Estimating Timber, Louis Margolin, Forestry Quarterly, Vol. XII, 
1914, p. 167. 



Fig. 62. — Method of running strips to cover 
an additional 20 per cent of area in heavily 
timbered tj'pe, on basis of original 5 per 
cent estimate for entire area. Strips 8 rods 
wide. 



294 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

But where strips are run at intervals of | mile and the timber is 
open and large, and especially in coniferous stands which have a fair 
degree of uniformity of sizes, although varying materially in density, 
it is possible to view the remaining timber without counting it or caliper- 
ing. If there were time for additional measurements, these would be 
made. The application of a correction factor is based on the assumption 
that the per cent actually measured is the maximum possible under 
the limiting conditions. Where an error would evidently be incuried 
unless the mechanical average is corrected, this correction should alwa} is 
be made. 

The method of applying this sort of a correction in the past has 
been as unsystematic as the ocular estimation of timber itself. The 
estimate from sample plots or strips was arbitrarily raised or lowered 
according to impressions obtained by the cruiser. This system may 
be greatly improved and a much higher per cent of accuracy obtained 
by observing the following principles: 

1. The comparison sought is not an absolute estimate of the volume 
per acre on the remaining area, but a percentage relation between this 
stand and the strip which is measured, by which the estimate on this 
remaining area may be obtained by increasing or duninishing that on the 
strip. 

2. The correction is an average for the whole area to be corrected, 
in the form of a per cent of total volume. Single observations must 
therefore be carefully weighted to obtain average results. 

3. The correction actually applies only to the area lying outside 
the strip and not measured. If applied to the entire area of the unit, 
the estimate on the strip itself is arbitarily raised by the same per- 
centage as applied to the residual area and this factor cannot be neglected 
in arriving at the proper per cent. 

To illustrate the last point, assume that 50 per cent of a tract has 
been estimated. By observation, the correction factor on the remainder 
is assumed as + 10 per cent. The estimate is 100,000 board feet on the 
strip. The correct estimate on the remaining area is therefore 110,000 
board feet and the total, 210,000 board feet. If 10 per cent is applied 
to the results obtained for the forty, the process would be, 100,000 
times 2 gives the uncorrected estimate for the area, or 200,000 board 
feet. A correction of 10 per cent gives 220,000 board feet, which is 
an error of 4.8 per cent in the estimate.^ 

1 This multiple, which in this illustration is 2, is sometimes termed the correction 
factor, but assumes no correction. It is merely the extension of the mechanical 
average over the entire area. For a 25 per cent estimate, the multiple is 4; for 
20 per cent, it is 5, etc. A method of applying the correction factor is in use, by which 
this multiple is raised or lowered. Where the multiple is 4, a +25 per cent correc- 
tion calls for 5; +12| per cent requires 4§, etc. 



THE USE OF CORRECTION FACTORS FOR VOLUME 295 

Since this error consists in applying the per cent erroneously to the 
area estimated within the strip, it diminishes with the per cent covered 
by the strip; e.g., should 25 per cent of the above tract be estimated 
and found to contain 50,000 board feet, and the correction factor be 
actually 10 per cent, the remaining area, which if uncorrected would 
have a stand of 150,000 board feet, has actually 10 per cent more than 
this or 165,000 board feet or a total for the tract, of 215,000 board feet. 
But applying 10 per cent to the entire tract indicates a total stand of 
220,000 board feet or an error of + 2.4 per cent. But with the decrease 
in the per cent tallied, the probability of obtaining a close observation 
of the remainder and applying a correct per cent also diminishes so 
that if a correction factor is used at all, there is less need for modifying 
the per cent. The conclusion is that when, on account of measuring 
a large per cent of the area, it is possible successfully to use a correction 
factor as applied to the remainder, there is all the greater necessity 
for making a correct application of this factor. 

To determine the actual correction from a per cent obtained by 
weighted observations, two methods may be used. The first of these 
methods applies to irregular areas where the per cent estimated is not 
uniform, that is, in areas estimated by the separation of types. The 
steps are as follows: 

1. Reduce the stand on strip to stand per acre. 

2. Apply the per cent correction to this stand per acre. 

3. Calculate the stand separately for the area not estimated, using 
the corrected average stand. 

4. Add together the estimates on and off the strip for the total; 
e.g., on 100 acres, 17 per cent is estimated and the remaining 83 acres 
is judged to run 10 per cent heavier than the strip. The tally on the 
strip is 170,000 board feet, averaging 10,000 board feet per acre. The 
10 per cent correction gives 11,000 board feet per acre off the strip, or 
a total estimate off strip of 913,000 board feet. The total, both on 
and off strip is 1,083,000 board feet. 

The second procedure may be applied when the per cent estimated 
is uniform and type or area correction seldom applied. The rule is, 
reduce the correction per cent by the proportion which the area estimated 
in the strip hears to the total area. E.g., where the strips cover one-half 
the area or 50 per cent, a correction factor of 10 per cent applies to the 
other 50 per cent or one-half. Then, .50X.10= .05. A 5 per cent cor- 
rection can be applied to the total normal estimate. Where 25 per cent 
is estimated and a 10 per cent correction is found, this applies only 
to three-quarters of the area; .75X.10 is .075. The correction factor 
of 7^ per cent may then be applied to the total area. It makes no dif- 
ference whether a correction of 10 per cent is applied to 75 per cent 



296 



IMPROVING THE ACCURACY OF TIMBER ESTIMATES 



of the area or 75 per cent of a correction of 10 per cent is applied to the 
whole area. 

Since the greatest danger in applying corrections to mechanical 
averages lies in failure to obtain a proper weighted average, and since 
it is better to let these mechanical averages stand rather than to intro- 
duce an unknown factor, dependent merely upon a guess, observations 
intended to demonstrate the need for a correction factor must be made 
as systematically as the strips themselves are run. Fixed points should 
be chosen at definite intervals along the strips at which to take these 
observations. These may be taken for instance at points 20 rods apart 
on the strip. At these points, the areas on either side of the strip 
should be compared with the stand upon the strip. 

The final result is expressed in terms of a per cent, but if each sepa- 
rate observation of a series is so expressed, the resultant per cent will 
not be weighted by the volumes to which its components apply; e.g., 
two successive observations may give the following result: 



Stand on strip 


Correction per 
cent 


Weighted volume 
correction 


10,000 
5,000 

Average of 2 plots 


+ 10 
-10 




+ 1000 
- 500 

+ 250 



The actual correction factor is +2^ per cent instead of zero. 

This principle of weighting the observations by volume is very 
simply applied. It consists of entering for each observation, not the 
per cent of comparison, but a comparison based on an ocular estimate 
of the stand per acre. The estimator puts down in two parallel columns, 
first the stand per acre estunated to be on the strip at that point, second, 
the stand per acre estimated to be on the remaining area. In arriving 
at this he includes as large an area as comes under his observation 
both on and off the strip. For double observations, i.e., taken on both 
sides of the strip, it is necessary to record the stand on the strip twice, 
once for each observation off strip. 

On the completion of the unit, these stands on and off strip are 
totaled. By dividing the total off strip by the total on strip, the true 
weighted volume correction factor is obtained. 

This factor is a percentage relation and therefore does not require 
that the ocular estimates per acre on which it is based be correct, pro- 
vided they are in the proper proportion. Each ocular guess may be 25 
per cent too low, yet the resultant correction factor will be, identical 



METHODS DEPENDENT ON USE OF PLOTS 297 

with that obtained if the ocular guess in each case were correct. This 
increases the probabihty of accuracy in applying the method. Actual 
tests of this principle have shown that where the average stand per acre 
off the strip differs as much as from 10 to 15 per cent from that on the 
the strip, under conditions permitting the inspection or actual seeing 
of the greater part of the timber, it is possible to reduce the error incurred 
by the mechanical average by at least one-half, provided the cruisers 
have some training and skill in application of the principle of ocular 
estimating. 

230. Methods Dependent on the Use of Plots Arbitrarily Located. 
In discussing the methods of estimating by means of sample plots, 
only the systematic or strip method of arrangement has been described. 
A second plan is to locate these plots arbitrarily by selection based upon 
individual judgment, the purpose being to get the total estimate by 
means of a few typical plots and greatly cut down the work required 
in systematic measurements. As in the strip systems, one of two things 
is done; either the plots which are measured are taken to represent 
the average stand per acre for the larger area of which they are a sample, 
or these plots are merely the basis of arriving at the stand by sub- 
sequent application of a correction factor. 

The first plan can be used only in conjunction with the area or type 
method in order to eliminate, as far as possible, variations in the stand 
by separating uniform and comparatively small areas. In this case, 
sample plots selected with care after a thorough inspection may be 
relied upon within reasonable limits of accuracy. By the second method, 
the plots chosen are seldom relied upon without further close inspec- 
tion of the stand. Cruisers using this method employ these plot 
measurements in order to establish in their minds the volume of typical 
stands having a definite density and appearance. Once fixed, this 
standard is used as a basis with which to compare the average stand 
on the area by exactly the same methods as were described under the 
correction factor in the strip method. The plots are merely much 
smaller and have more definite standards than the strips, and their 
application to the larger area is more difficult. The use of these plots is 
still further restricted, with improved accuracy, when they are intended 
merely to determine the volume of the average tree of certain classes 
of timber, and the estimate on the remaining area is determined by a 
tree count covering practically 100 per cent. 

Various combinations of the above plans are used, especially in the 
South, by cruisers working in pine in an effort to cover the ground 
accurately with a minimum of time and expense. 

231. Estimating the Quality of Standing Timber. An estimate of 
standing timber is in effect an inventory of raw materials intended 



298 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

to establish the total value of the stock on hand. It is not sufficient 
to know the quantity of wood in the forest in terms of board feet or 
cubic feet. The estimation of poles, ties and other piece products 
by sizes and grades illustrates this need. An inventory requires a 
statement of the total quantity of each class of product, and of each 
grade or quality within that class, which has a different unit price or 
value. 

Lumber grades differ enormously in value (§ 352), and the quantity 
of separate grades of lumber which may be sawed from trees of different 
ages and sizes differs as widely as their values. The estimation of the 
amount of the different standard grades of lumber in standing timber 
is as essential in determining its value as the measurement of the total 
quantity in board feet. The neglect or inability of many foresters, 
whose training was along lines of mechanical estimating (§ 223) to 
determine the amount of the product by grades has done much to 
withhold a recognition among practical cruisers of the great services 
rendered the profession of cruising by foresters in contributing volume 
tables and in systematizing the making of topographic maps. 

What is wanted is the estimation of the total quantity of timber 
on a tract, separated into the amount of each of several standard grades, 
covering the range of the products and sufficient to include practically 
the enthe cut and to determine its average value on the stump. This 
problem is closely related to that of discounting for defects in that both 
require a close observation of the character of the standing timber 
rather than its mere dimensions. 

All defects which reduce the value of sawed lumber reduce its grade. 
When these defects are of a character to reduce the grade below a certain 
standard (§ 358, Appendix A), the material is no longer scaled under 
the rule of sound scale. It may still be sawed and sold as lumber. 
But when it ceases to hold together as boards it is cull. 

The deduction of a per cent of the total estimate for defects brings 
the estimate into conformity with the quantitative " sound " scale. 
The further separation into grades of the sound portion of the timber 
which will be scaled and estimated, recognizes the influence of defects, 
chiefly knots, but including other classes, such as wormholes, sound 
stain, and twisted grain, which lower the grades and nature of the 
log contents (§ 352, Appendix A), 

To determine grades, a knowledge of the results of sawing and the 
study of logs as they are opened up and graded into products on the 
sorting table is far more valuable than the experience gained in studying 
the apparent defects of standing timber. This knowledge must then 
be supplemented by a knowledge of the growth of trees in stands. 
Open-grown trees, although large, are of low quality due to the presence 



METHOD OF MILL RUN APPLIED TO THE STAND 299 

of knots, while trees grown in dense stands have a higher per cent of 
upper grades due to the history of their development. The skill required 
in judging the per cent of grades in standing timber is based directly 
on these two sources of information and is not a matter of guess work. 

232. Method of Mill Run Applied to the Stand. Data on grades 
produced in sawing takes two forms; the total output by grades for 
mills sawing in a given region and character of timber, and the specific 
contents of logs of different sizes and quality, as determined by mill- 
scale studies (§361, Appendix A). This corresponds with two dif- 
ferent methods of applying the information on grades to the standing 
timber, namely, application to the stand as a unit, and application 
to the tree or log units. 

In applying mill-run grade per cents to the stand, the total estimate 
in board feet is arbitrarily divided into the different grades which it 
will probably yield, by per cents of this total. This method corresponds 
with that of ocular estimate of a stand (§ 206) and its results are about 
equally um-eliable. The basis is the sawed output by grades from mills 
in the vicinity. These per cents so obtained will apply to the timber 
in question, only if it happens to average the same in quality as that 
sawed, which assumption, considering the great variation in standing 
timber, is wholly untrustworthy. This means that the per cents of 
grade must be modified as the timber is better or poorer than that 
sawed, which requires a knowledge of the standing timber previous 
to sawing. 

233. Method of Graded Volume Tables Applied to the Tree. Evi- 
dently, a better basis is required and, just as in timber estimating for 
volume, this must be found in the use of the tree unit or the log unit, 
by which the varying quality of the timber can be standardized. 

The tree unit has not proved a satisfactory basis for grading, though 
it is possible to use it. The basis is graded volume tables (§ 165) which 
show the per cent of standard grades in trees of different diameters, 
preferably in the form of per cents of contents. 

These per cents could be applied to the trees in each diameter class 
and the total estimate divided in this way into the component grades. 

The objection to this method is that it is not sufficiently elastic 
to take care of the great range of quality in trees of the same diameters. 
A given graded table will hold good only for timber of a certain character; 
if more open-grown, shorter boiled or limbier, or otherwise different, 
the volume table is not applicable. The method is probably better 
than the ocular guess, but is equally subject to large corrections in the 
field. 

234. Method of Graded Log Rules Applied to the Log. The third 
method employs the log as the basis of grades, and applies this basis 



300 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

to the standing timber. The graded log table (§ 74) appears to 
satisfy the requirements of the problem. Log grades are such as can 
be recognized in standing trees, on the basis of diameter, surface appear- 
ance, presence of knots or limbs, and character of the tree and the stand 
in which it is growing. In turn, these log grades can be analyzed by 
mill-scale studies, so that the average per cent of grades of timber in 
each log grade is known. Since three grades are usually made in valu- 
able species, and at least two for the less valuable, trees of the same 
D.B.H. can easily be thrown into the lumber grades corresponding 
with differences in their character, by recording the logs which they 
contain as grades No. 1, 2 or 3. By contrast, if graded volume tables 
are used, ordinarily only one classification is available for the tree — 
that corresponding with the table. 

The final problem is the application of these graded log tables to 
the standing timber, in a manner to conform to the methods used in 
timber estimating. Cruisers who use the method of selecting an aver- 
age tree (§ 209) usually analyze this tree by the use of the log gi'ades, 
or directly by per cents, into the grades of lumber which they believe 
it will cut, and apply these per cents to the remainder of the stand. 
This is a crude method. 

Where the method of tallying the diameter of every log (§ 119) is 
used, each log can be tallied under its proper log grade. The total 
volume in each log grade is thus obtained directly. Where timber 
is sold as logs, it is unnecessary to go beyond this point. 

But where the sawed product determines stumpage value, these 
log grades are merely the basis of application to the standing trees of 
the grades of lumber which they probably contain, and the contents 
of the log grades, in lumber of each grade, will be computed for the 
estimate. 

235. Combination Method Based on Sample Plots and Log Tally, 
Where the tree tally and volume tables are used in estimating (§ 121), 
the application of the log-grade unit to each tree is not possible, since 
it would mean a shift to the tally of logs and not trees. Here a com- 
bination method is necessitated, based on the principle that grades 
or quality of timber can be determined by the measurement of a much 
smaller per cent of the total volume than is required for volume estimate. 

The method is to lay out sample or representative areas in the form 
of strips crossing the types as for timber estimating (§ 209) and com- 
prising a per cent of the area estimated, sufficient in the judgment of 
the cruiser to obtain the average quality sought. On these areas, 
every log in each tree is totaled by upper diameter, in the log grade 
in which it belongs. Instead of guessing at these upper diameters, 
taper tables based on D.B.H. (§ 167) and total, or merchantable, heights, 



LIMITS OF ACCURACY IN TIMBER ESTIMATING 301 

possible if the latter are cut to a fixed diameter, or if made to conform 
to average utilization, are used to get these diameters; e.g., for a tree 
38 inches D.B.H. containing eight logs, the upper diameters are 
respectively, from the table, 32, 30, 28, 25, 22, 18, 14, and 10 inches, 
and are so recorded, each log under its proper log grade. (See § 207 
for form of tally.) 

The determination of the number of board feet of each standard 
grade in logs of each diameter and grade, and the total scale for each 
lumber grade, is based on the contents given for these log grades from 
mill-scale studies of log contents. The purpose is to obtain the per 
cent of each grade, regarding the total contents of the logs tallied as 
100 per cent, and then to apply these per cents to the volume estimated 
for the tract. These per cents can be obtained more accurately if over- 
run is included in logs of each separate size (§46). The mill-scale 
study will show the amount of over-run in logs of different diameters 
and standard lengths. The scaled volume of these logs should then be 
increased by this per cent of over-run, before the division into lumber 
grades is made. On the total sawed contents thus obtained, the per 
cent of each grade is based. ^ 

Even if considerably in error, the value of an estimate expressed 
by grades of lumber is much greater than one which entirely ignores 
the quality and consequently the relative stumpage value of the tract. 

In the absence of specific information on grades, a record of the sizes 
of the trees, their clearness of bole, and the density of the stand may 
furnish a basis for approximating the probable grades. 

236. Limits of Accuracy in Timber Estimating. Purely ocular 
estimates vary in accuracy up to errors of 100 per cent, dependent 
upon how far the method is stretched from its original limitations. 
This does not include errors due to inexperience, inefficiency or careless- 
ness. 

In mechanical methods of measurements, serious errors may occur 
in computations. Such errors, of course, are inexcusable, but their 
avoidance requires careful checking. The mechanical errors due to 
the operation of the law of averages have been pointed out as a function 
of the factors influencing these averages, the chief of which is the size 
of the area unit. 

The degree of accuracy must be based upon the standard of utiliz- 
ation. It is entirely unfair to judge the accuracy of estimates based 
upon one standard against the results of sawing attained by the appli- 
cation of an entirely different standard. Wliere the standard is the 
same in both cases, the present demands of timber estimating require 

1 The details of this method are taken from the article by Swift Berry, Journal 
of Forestry, Vol. XV, 1917, p. 438. 



302 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

an accuracy of within 10 per cent. The error should be conservative 
rather than an over-estimate if possible. Greater errors than 10 per 
cent may be caused by differences in scahng practice alone, or in the 
length of logs cut, or the thickness of lumber sawed. 

237. The Cost of Estimating Timber. No figures will be given for 
the costs of various methods of timber estimating. These must be 
determined locally. The elements of cost are: 

1. The size of the crew and the wages paid each member; the 
character of supervision, such as the combining of several crews under 
one supervisor; and the employment of a cook. 

2. Accessibility of the tract as affecting transportation of men and 
of supplies, especially of food. The means of transportation, such as 
pack versus wagon haul. 

3. Cost of location of boundaries and surveys and cost of establish- 
ment of base lines from which strip surveys are to be run. This is a 
function of the size of the tract and the character of the boundary survey 
and monuments already established. 

4. The number of strips or miles of line to be run per unit of area. 
The cost is not exactly proportional to the miles run since certain 
items such as travel to and from work and from one strip to another, 
cost of computing the estimate, and cost of mapping in the office, increase 
in a lesser ratio. Doubling the number of strips increases the cost from 
50 to 80 per cent, dependent upon the saving in these items. 

5. The rapidity of traverse or number of miles of line which may be 
run per day. A standard day's work varies directly with topography 
and brush, and with the amount of detailed work required in the actual 
estimate along the strip, as determined by the number of products, 
the number of species, the number of trees and the details of record 
required. In very brushy and mountainous or precipitous country 
with a variety of species, 1 mile per day may be all that is possible, 
varying up to 2 miles. An average day's work in fairly open country 
varies from 2 to 4 miles; on level open land with sparse timber and no 
brush, 4 to 8 miles may be made. 

6. The character of the topographic map required. To a certain 
extent, a detailed topographic map appreciably slows up the work. 
It is the object of a forest survey to requu-e only that degree of accuracy 
and detail which will not add appreciably to the cost by delaying the 
party. 

7. Computation or office work required. By practical cruisers, this 
is almost eliminated through the methods employed. Methods of 
tallying dimensions and the use of volume tables increase this addi- 
tional expense. 

8. Holidays, sickness and lost time. Only the number of hours 



TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 303 

on the actual work of running lines and estimating can be considered 
as the basis of costs. All lost time ,for any other cause adds to the 
costs per hour of work. 

9. Personal efficiency. The training and personal efficiency of the 
men employed may make from 25 to 50 per cent difference in the actual 
cost of the work, but its principal effect is in greatly increasing the 
relative accuracy of the estimate. 

Cost of estimating should be computed as follows: 

Total cost itemized under salaries, and cost of supplies, transporta- 
tion and subsistence. 

Cost reduced to the cost per hour of actual work by dividing this 
total by the number of hours employed in estimating. These costs 
can be separated into field work and office work, including mapping. 
The costs can then be expressed as cost per unit of area or per acre 
and finally as cost per unit of product, as per thousand feet or per 
cord. This is the final test of cost. The cost should then be compared 
with the stumpage value per unit. If possible it should not exceed 
1 per cent of this value. 

238. Methods of Training Required to Produce Efficient Timber 
Cruisers. Mechanical methods of timber estimating, dependent upon 
the measurement of diameters and heights with instruments, and secur- 
ing the mechanical average stand per acre by strips, do not require 
anything more than conscientious work and care in details. Skill and 
training enter with the application of the laws of averages, even for the 
construction of height curves. The demand for training is increased 
by the use of ocular methods of measurement and reaches its maximum 
in the application of cull for defects and in judging the quality of timber. 
Aside from Tamiliarity with cull and grades, there are no principles of 
timl^er estimating that cannot be learned in a month's intensive train- 
ing. The common impression that it takes several years to develop 
ability as a timber cruiser is based upon the unscientific methods 
employed in training these men. They usually acquire their skill by 
a maximum of hard work in the woods, with a minimum of accurate 
comparisons of the estimated volumes with an actual cut. Even in 
the matter of judging defect, the basic training should not be in the 
woods, but in the mill and in scaling. It is comparatively easy to recog- 
nize the signs of defect in standing timber, but much more difficult to 
judge of the amount of cull which it causes. In actual training of 
timber cruisers it has been found that ability to secure accurate esti- 
mates is greatest in men who have best developed their mental faculties 
by education, close observation, memory and systematic coordination. 
This same combination of qualities is desirable for success in any line. 
Many cruisers lack this ability and remain permanently inefficient tO 



304 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

a marked degree. The only reason that such individuals have in the 
past continued to practice timber cruising as a profession is the almost 
complete absence of a reliable check on their results for years at a 
stretch, and the comparative indifference of purchasers to the accuracy 
of estimates due to a rising market and a plentiful lumber supply. 

Standing timber cannot be " measured." There is always a residual 
error in the closest work. Hence the use of the term " estimates." 
Although the only basic check on estimates is the measurement of the 
timber after it is cut, yet it is possible, by the use of intensive methods, 
to measure plots of standing timber so closely that they will serve as 
checks on individual estimators. 

An example of this check is cited below in the case of a Minnesota lumber com- 
pany, which in 1907 required each of its timber cruisers to estimate an area which 
had previously been carefully calipered and measured with a volume table and was 
afterwards cut and checked out with these measurements. The results speak for 
themselves. These men were given all the time they desired to make this estimate. 



TABLE XLV 

Comparative Estimates on a Tract of 40 Acres 

Board Feet 





Calipered, 

and 

measured 

by volume 

table. 

Defects 

deducted 


Estimators, by Individual Methods 




No. 1* 


No. 2 


No. 3 


No. 4 


White pine 

Norway pine 

Spruce 

Tamarack 

Jack pine 

Balsam 

Hardwoods 


2.50,800 
4,120 
9,870 
35,480 
730 
2,220 
9,910 


220,000 
23,000 


300,000 
45,000 


400,000 

35,000 
3,000 


130,000 

10,000 
10,000 
15,000 


Total 


313,130 


243,000 


345,000 


438,000 


165,000 


White pine f 


No. 5 


No. 6 


No. 7 


No. 8 










199,000 


175,000 


125,000 


115,000 



♦ Number of cruiser. t No other species estimated by these four cruisers. 



TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 305 

The tract, when cut, scaled by Scribner Decimal C log rule 314,350 board feet, 
an error of tV of 1 per cent. 

The best system of training men for timber estimating is by the use of sample 
plots on which the diameter and merchantable heights in log lengths of each tree 
are estimated by the eye and checked against the records. On these same plots, 
each of the six classes of averages (§ 209) can then be tested and their application 
mastered. Each day's training can be checked against the measured volume of 
the plot that night and not only the total error in per cent but the exact cause of 
this error ascertained. On this basis, the progress of training is rapid and the 
cruiser is advanced in a short time more than would be possible in several years of 
estimating without these checks. The following outline will illustrate the possi- 
bilities : 

1. Plots of 20 acres, 40 by 80 rods, are laid out with compass. The boundaries 
are marked by blazing the trees facing each of the four sides on the face towards the 
plot. Stakes are set on all four sides at distances of 20 rods apart. Two plots are 
laid out adjoining each other, together comprising 40 acres. 

2. Every tree on the plot is calipered at B.H. in two directions, the average 
being taken to the nearest even inch and the bark blazed to prevent duplication. 
The blazes are made facing the portion or strip not yet measured. A crew of one 
tally man and two caliper men are used and all trees above a fixed diameter are taken, 
corresponding Avith the minimum exploitable diameter class. 

3. The merchantable heights to the nearest 8-foot length or half-log are measured 
by two or three additional men with Faustmann hypsometers. From 30 to 40 per 
cent of all heights can be measured during calipering in this way. Height men 
work mth the diameter crew taking the diameter as measured, pacing for distance 
from the tree and recording heights based on diameter. Forty to sixty heights 
per hour can be recorded by each man. Upper diameters or merchantable lengths 
are based upon the practice of sawing as applied to the species measured, provided 
this is the basis on which the voliune table was constructed. 

4. The determination of the merchantable height of every tree from that of 30 to 
40 per cent of the trees is made separately for each diameter class. The heights 
tallied within the diameter class are taken to indicate the percentage or proportion 
of the different height classes existing in this diameter class and the total number 
of trees are then distributed according to the same proportion. As the result required 
is a proper distribution for the plot as a whole, and not for each diameter separately, 
this method gives a sufficient degree of accuracy. 

5. The record for the plot will show the following data : total estimate in board 
feet, total number of trees, average stand per acre, volume of average tree, volume 
of average log or log run per thousand board feet, exact number of trees in each 
diameter class, exact number of trees in each log and half -log height class independent 
of diameter. 

The exact number of trees in each separate diameter and height class is the 
basis for the last two summaries ; but the summaries rather than the detailed class- 
ification are made the basis of the estimating, i.e., the tally is totaled for each 
diameter class, and in turn, is totaled for each height class irrespective of diameter. 

For each day's work the cruiser hands in a report on the first five of the above 
seven items and brings in his notebook In which he has totaled the number of trees 
for each diameter class and each height class separately. His accuracy is computed 
as a per cent of the total stand on the plot. The error in per cent is recorded. The 
sources of error are then examined. These are four in number. 

1. The width of the strip may be too great or too small. This is shown by an 
error in the number of trees tallied. 



306 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

2. The trees may not be counted accurately. This error is identical with the 
first, but usually shows up as a deficiency of small timber near the minimum diameter 
tallied. 

3. The diameter of the trees may be over- or under-estimated either as a whole, 
or in certain classes. There is a strong tendency to bunch diameters towards a tree 
whose size seems to be the standard in the cruiser's mind. This results in over- 
estimate of small trees and under-estimate of trees of larger diameters. 

4. The heights may be over- or under-estimated. When this happens it shows 
up consistently for the whole tract, the standard of height apparently being tem- 
porarily distorted in the mind of the cruiser. 

A fifth source of error, the volume table and the failure to coordinate upper 
diameters and merchantable lengths with the standard used in this table, serves 
to exaggerate the per cent of error in the judgment of heights, but is always indi- 
cated when the average heights are too high or too low to agree with the measure- 
ments. When the volume of the average tree is high or low, it usually means an 
over- or under-estimate of diameters or heights. The exact character of the error 
in diameter and height is ascertained by a simple check as follows: the cruiser com- 
pares the number of trees in each diameter class with that of the standard record and 
sets down his difference plus or minus. If he is over-estimating, but has the right 
number of trees, the minus sign -mil appear opposite the smaller diameters and the 
larger diameters will show excess numbers. If under-estimating, the plus signs 
will appear opposite the small diameters. The same rule applies to heights. An 
over-estimate causes minus signs to appear opposite the lower height classes and 
corresponding plus numbers in those of greater log lengths. The size of these dis- 
crepancies shows the degree to which the error has been carried. 

It is the tendency in cruising as in scaling logs, in an effort to correct a known 
error, to incur immediately a still greater error in the opposite direction; but when it 
is possible to check against a measurement which the cruiser admits is infallible and 
in which he has confidence, this tendency to fluctuation is soon overcome and rapid 
improvement is noted, not only in the total per cent of accuracy which is sometimes 
merely the result of large compensating plus or minus errors, but in each of the four 
elements of accuracy, thus insuring a consistent degree of accuracy from day to day. 

The cruiser is expected to master but one detail at a time, and the schedule 
is as follows: 

1. During the calipering of the standard plots, the eye is trained in estimating 
diameters which are then promptly checked by the measurements. The same is 
true of heights. 

2. The second period is devoted to a total or 100 per cent tree by tree estimate 
with a tally of each diameter and merchantable length. The total area of the 
plot is covered by eight strips, 5 rods wide, the cruiser working not in the center, but 
on one side of this strip with compassman marking the opposite border. Width of 
strip and success in getting 100 per cent of the area is dependent absolutely upon 
use of eye, checked by pacing and judging distance, and the men are not permittee) 
to mark the boundaries of these strips to prevent overlapping. Twenty acres per 
day are covered by this method. 

3. The third step is to increase the area covered per day to 30 acres by doubling 
the width of the strip to 10 rods, the cruiser taking the middle of the strip and judging 
5-rod distance on each side. In all of this work, the cruiser tallies his own dimen- 
sions of the trees. In these preliminary 100 per cent estimates, constant repeated 
checks are made of the diameters and heights to continue the improvement of the 
eye. 

4. The 100 per cent estimate is continued, but the tally of every diameter is 



TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 307 



discontinued and a total count substituted with a tally of one tree in three. The 
area is increased to 60 acres per day. It is the universal testimony of cruisers 
that this simplification of the tally relieves the mind of a strain and improves the 
accuracy of the dimensions tallied and consequently of the total estimate. It has 
been found that an average volume is obtained through a tally of one-tlxird of the 
stand under the following conditions : 

When there are at least 500 trees per 40 acres of the species tallied and preferably 
1000. 

When the judgment or process of selection is entirely eliminated in favor of 
mechanical selection of the trees to be tallied. This may be done by taking every 
third tree in succession or by taking the nearest tree in each case. Where there are 
insufficient trees to insure the mechanical average, or where the range of size is large, 
the count may be separated into two groups, segregating the large from the small 
trees, one tree in three tallied separately in each group. This adds very little to 
the detail required when working with a single species. 

5. Only 50 per cent of the area is estimated by the above method. The area per 
day is nominally 120 acres. The remaining area is inspected by eye at distance of 
20, 40 and 60 rods in order to apply a weighted 

volume correction factor as described in § 229. 
In this method, four strips are run, each 10 rods 
wide, as before, starting from points, 5, 25, 45, 
and 65 rods from the corner and alternating 
with strips not estimated as per Fig. 63. 

In order to check the correction factor, the 
alternate strips not previously estimated are now 
in turn estimated, keeping the record separate 
from the original four strips. The correction 
factor derived from observation is first com- 
puted and the corrected estimate is then com 
pared with the tally of the strips estimated. 

6. Up to this time no effort has been made 
to deduct for cull which would introduce an 
arbitrary factor interfering with the comparison 
of the work of the cruiser with the measurement 
of the plot, both of which have been on basis 
of sound contents, disregarding possible cull. 

The cull factor is now tested by close examination of 10 acres in which every tree 
is individually estimated and the per cent of probable cull recorded and subtracted 
from the estimate. Per cent figures also are obtained from the scale of logs of 
similar timber in the vicinity and these per cents are used as a basis of cruising. 

7. In actual cruising, the per cent of area covered is reduced to 25. The area 
is increased to 320 acres per day, and 4 miles of line rmi. A cull factor is used and 
hardwoods are added to the estimate by tallying the top diameter of each mer- 
chantable log, inside the bark. 

8. The cruiser is then brought back to the sample plots to receive training in 
individual estimating. This consists of: 

The use of circular plots covering different per cents of the area by a systematic 
plot method and finally by the selection of a sample plot by eye. On these plots, 
he first arrives at the volume of the average tree either by direct approximation or 
by selection of a typical tree whose volume is ascertained from a volume table; 

A tally of the diameter and height of each tree on the plot and the immediate" 
computation of the volume to ascertain the true average tree for comparison with 




Fig. 63. — Method of estimating a 
forty by use of the correction 
factor. Points at which obser- 
vations are taken shown by 
dots. 



308 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

the ocular guess. Two days of this work will greatly improve the ability of the cruiser 
to substitute ocular methods for measurements. 

An opportunity to run out strip estimates in which he does his own compass work, 
counting the trees ahead of him in rectangular blocks. The volume of these trees 
is obtained: 

By the log-run method of estimating the number of logs m the average tree 
and the average contents of the log or log run per thousand; 

By selecting an average tree in volume for each of eight separate strips, the 
total tally of which is kept separate. This principle could, after practice, be applied 
to the entire forty, or to separate groups. 

The exact details of this system as to size of sample plots, widths of strip and 
methods of tallying heights were worked out for Southern yellow pine, and several 
of these points would need modification if applied to timber of radically different 
type and conditions. But the general method of careful, original measurement 
of the control plots and of proceeding from a 100 per cent intensive estimate 
through various stages of less intensive work in which the six classes of averages 
are employed as substitutes for the full tally, can be worked out for any forest 
type and form the basis of rapid and practical training in the art of timber 
cruising. 

239. Check Estimating. Just as in the training of a cruiser his 
greatest drawback is lack of any check on his estimates, so check esti- 
mating does not benefit the cruiser unless he can be told, not only what 
the extent of his error is, but just how he made it. Check estimating 
must depend either upon the infallibility of the check estimator, which 
may be questioned in the mind of the person checked, or by the sub- 
stitution of actual measurements on a basis which removes all source 
of doubt, leaving only cull and quality to be judged. Check estimates 
should therefore be made on definite areas or strips, prevously or sub- 
sequently estimated by the cruiser and on which a record has been kept 
similar to that indicated in the description of the methods of training 
timber cruisers. The tree count, the total volume, the average volume 
per tree, but most important, the tendency to over-estimate heights 
and diameters should all be checked separately. When this is done, 
one of two things will happen. Either the cruiser will rapidly acquire 
a much greater accuracy or he will demonstrate his complete unfitness 
for the job of timber cruising and can be put on other work. 

240. Superficial or Extensive Estimates. The preliminary examina- 
tion of a tract of land for the purpose of determining roughly whether 
it has timber of value and approximately how much, calls for the exercise 
of the maximum of skill and experience in order to attain a reasonable 
degree of accuracy in the minimum of time allowed. 

A description of the estimation of a tract of 2300 acres for the Blooming Grove 
Hunting and Fishing Club, located in Pike County, Pennsylvania, will serve as an 
illustration of methods possible in such an examination. The field work on Taylor's 
Creek logging unit occupied two days including travel to and from the unit. Not 
much over one day was put on the estimate itself. The fundamental basis of the 



CHECK ESTIMATING 



309 



methods employed was the location of corners with the aid of a guide, the use of a 
map and the sketching of the boundaries of areas of different types by intersection, 
aided by rough triangulation from known points. Cardinal directions for strips were 
not attempted in any instance. This tract was afterwards estimated by the strip 
method, running 5 per cent of the area. The comparison of the two methods arid 

TABLE XLVI 

Estimate of Taylor's Creek Logging Unit, Blooming Grove Tract, Pike 

County, Pa., 1911 

A. By extensive methods, in two days' time, one inan with guide. 

B. By 4-rod strip, 5 per cent of area, diameters calipered, average heights. 



. 










Error by First 












Method 




Area. 




Method of cruising 


Estimate. 






Type 


Species 


employed under 














A 


M feet 


Amount. 
M feet 


Per cent 




Acres 






B.M. 


B.M. 




Pitch pine. 


375 


Pitch pine 


j-acre circular plots 


A 2178 


- 36 


- 1.7 


pure stands 






for sizes 
8-rodrectangularplots 
counted, when con- 
venient 


B2214 






scattered on 


1275 


Pitch pine 


16-rod strip counted. 








burns 






when convenient 








White oak and 


200 


White oak 


Total count of large 


A 248 


-197 


- 47 


hardwoods 






trees 
Average trees guessed 
at 


B 445 






Swamps with 


450 


Spruce 


j-acre circular plots, 


A 750 


+353 


+ 88 


har dwoo d 






selected by guess for 


B 397 






and conifers 






average stand per 
acre 












Hemlock 




A 750 
B 527 


+223 


+ 42 












Yellow 


Some poplar coimted 


A 250 


+ 161 


+181 






poplar 




B, 89 










Ash 




A 100 
B 125 


- 25 


- 20 












White 


Treetops counted 


A 250 


- 32 


- 11.3 






pine 


from hill. Average 
tree guessed at 
Uniform old growth 


B 282 






Total 


2300 


A 4526 


+526 


+ 10.9 










B4079 


' 





310 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

their results is made on the basis of the assumption that accurate results on this 
area were obtained by the strip method. The cost of the original estimate was $60.00 
or 2.6^ per acre, l.S^ per thousand. The cost of the subsequent strip estimate 
was 8^ per acre or 4«f per thousand. The results clearly show that the average stand 
per acre was successfully obtained for the pitch pine types in which the timber could 
be seen, and where the area was carefully mapped in two degrees of density of stock- 
ing and checked by strips and plots carefully selected there was no need of a subse- 
quent estimate. 

The method of counting every tree was successful for white pine since all of the 
tree tops were seen and the average tree was correctly guessed at, but for white oak, 
the total count apparently failed. This was due not to a defect in the method or 
its application, but to the fact that 123,000 feet of white oak was found later con- 
cealed in the swamps. This reduced the error to 23 per cent for the portion seen 
and counted. 

The estimate of spruce, hemlock and poplar broke down because of the funda- 
mental difficulty of applying the sample plot method when based upon selection 
and not on systematic arrangement. The swamp should have been crossed and all 
parts examined. As it was, the sample plots were selected near the boundary where 
the timber was one-half to two-thirds again as heavy a stand per acre as in the wetter 
portions. This resulted in over-estimating spruce, hemlock and poplar. An 
area or density correction here, or another day spent on that portion of the tract 
would have greatly reduced this error. 

In extensive mapping and estimating of large areas for purposes 
of classification as in the preliminary examinations for the establish- 
ment of national forests, rough sketch maps of the areas of timber 
types are made on the above principles by location of the cruiser on 
a map and by triangulation. The estimate must depend upon the 
location of occasional sample plots chosen with the best skill possible 
to get average stands. 

In State work the construction of maps showing the timber resources 
of the State or of various counties is usually carried on by similar 
methods of mapping, using roads and the principle of the wheel or 
odometer for distances and sample plots for average stands. In Massa- 
chusetts a different principle is employed. Strips 4 rods wide are run 
at |-mile intervals on which detailed measurements are taken of the 
stand. No attempt is made to complete the map of timber in the inter- 
vening areas, but the data are assumed to show the average for an entire 
town, an assumption which is probably correct owing to the large 
area involved. 

241. Estimating by Means of Felled Sample Trees. In the absence 
of volume tables in earlier European practice, it was found that volume 
of stands could be determined by calculating the diameter of the aver- 
age tree, felling it and determining the cubic volume. This volume 
multiplied by the number of trees in the stand was supposed to give 
the number of cubic feet in the entire stand. Since height and form 
factor of individual trees both varied over a wide range, it was quite 



METHOD OF DETERMINING THE DIMENSIONS OF A TREE 311 

difficult to get a tree which was actually an average for the stand, but 
when the stand was divided into diameter groups, any required degree 
of accuracy could be obtained, according to the number of groups made. 

In determining the diameter of the average tree, the arithmetical 
mean of diameters gave too small a result since the volumes of trees 
of uniform height are in proportion to D'^. With a table of the areas of 
circles, the total basal area or sum of the areas of the cross sections at 
D.B.H. for all the trees on the plot was obtained and divided by the 
number to obtain the average basal area. The diameter correspond- 
ing to this basal area was that of the tree sought. Where a tree of this 
exact diameter to yV-inch could not be found, a larger or smaller tree 
was selected and the difference found by the proportion existing between 
the basal areas of the tree measured and the tree desired. This method 
is termed the Mean Sample Tree Method. 

In this country the application of these methods has been confined 
to a few early investigations into the cubic volume of cordwood in second- 
growth hardwoods. The difficulty of selecting a tree of average height 
and form as well as basal area and the expense of felling and measuring 
a tree makes the use of volume tables far preferable whenever these 
are dependable, and their substitution is practically universal.^ 

242. Method of Determining the Dimensions of a Tree Contain- 
ing the Average Board-foot Volume. Another use of sample trees is 
in connection with the determination of the age and growth of stands 
rather than to determine their volume. For this purpose, the volume 
of the stand is first found from volume tables and the average tree then 
determined. The volume sought is that of a tree which when multi- 
plied by the number of trees on the plot, will give the total volume of 
the plot in the unit of volume which was used in estimating. 

1 A recent test, 1920, by J. Nelson Spaeth, Harvard Forest School, in second- 
growth hardwoods, in which mean sample trees for each 3-inch diameter group 
were measured, gave the following comparison of accuracy with the use of a standard 
volume table, although the latter was for but one species, red maple, comprising but 
15 per cent of the stand : 



Method 


Yields per ^ acre. 
Cords 


Error. 
Per cent 


Actual volume cut 


5.725 

5.772 
5.935 




Standard volume table 


+1.70 


Mean sample tree method 


-f-3.84 







The refinements of these methods, known as Draught's, Urich's and Hartig's 
Methods, are set forth in Graves' Mensuration, pp. 224-242. For application to 
American problems that of the Mean Sample Tree is probably sufficient. 



312 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

Wlien cubic volume is used the average tree will not be the same 
in diameter as when the board-foot unit is employed. The explanation 
for this difference is that the volume sought is a weighted average of 
the merchantable contents of all of the trees on the plot. Trees of 
different diameters do not have the same weight in this average when 
measured for board feet as when measured for cubic contents. The 
tree containing the average board-foot volume will be larger than the 
other. The smaller trees in the stand when measured in board feet 
are more immature than they are for cubic feet and the merchantable 
portion of the stand actually includes a lesser proportion of the whole. 
In stands which are not of even age, this merchantable portion would 
exclude many of the younger trees as being umuerchantable although 
they would be included in the cubic volume, and the average age as 
well as size of the portion merchantable for board feet is greater than 
that included in the cubic volume. (The increase in average age of 
stands due solely to the exclusion of a portion of the stand is a recog- 
nized fact in European practice.) 

To determine the size as well as volume of the average tree of a 
stand, we have two variables, height and diameter, one of which must 
be fixed or eliminated before the other can be determined. The first 
step is, therefore, to determine the average height of trees of each diam- 
eter by a height curve (§ 209). The average tree can then have but a 
single height and diameter and these dimensions may be found from 
a curve of volume based on diameter for the plot. 

This curve may be taken from a standard volume based on diam- 
eter and height (§ 143) by selecting the volumes corresponding to the 
average heights for each diameter interpolated if necessary to the 
nearest foot. At only one point on this curve will the average volume 
coincide with the diameter. 

243. The Measurement of Permanent Sample Plots. The purpose 
of locating and measm-ing permanent sample plots is to determine the 
growth of stands. Their original measurement therefore must be made 
by methods which will permit of an exact scientific comparison of these 
with subsequent measurements. In this way, not only can the growth 
of individual trees be determined, but all changes which take place in 
the forest by decadence and by the operation of natural forces, insects, 
fungi and cutting and thinning, or other silvicultural measures may be 
noted. 

Permanent sample plots should be located on land under perma- 
nent and stable ownership and should be accessible and easily found for 
subsequent inspection and for a maximum of protection. The plot 
should be square or rectangular and marked by permanent corners, 
plainly labeled. Sample plots should be located in stands having 



THE MEASUREMENT OF PERMANENT SAMPLE PLOTS 313 

uniform conditions and their size should be governed, first, by the 
possibility of securing this uniformity and second, by the expense of 
measurement which limits the size of the plot. Third, wherever 
possible, there should be a control strip of exactly similar timber sur- 
rounding the plot on all four sides in order to eliminate the influence 
of different conditions of density or site around the borders of the plot. 

The merchantable timber on these plots is measured as follows: 

Tree Number. Each tree should be permanently numbered either 
by white paint or by attaching a metal tag to the tree with a copper 
nail. 

D.B.H. The point at D.B.H. is measured and spotted with white 
paint or by the position of the tag. The D.B.H. is measured with a 
diameter tape. 

Crown Class. The crown class is one of the following: 

a: = trees standing alone; 

d = dominant; 

c = co-dominant; 

i = intermediate ; 

s = over-topped, suppressed. 

Height. The height is measured to the nearest even foot with a 
standard hypsometer. The Klaussner principle, which gives one 
measurement, is preferred.^ 

Forms are used which provide, for each tree, five vertical columns 
in which to record the original and four subsequent measurements 
which are taken at either 5- or 10-year intervals. 

The trees on such plots are usually numbered and measured indi- 
vidually down to 4 inches, although in some instances 2 inches is 
adopted as the basis for individual tree records. 

Immature timber below these sizes usually calls for smaller plots 
which are sometimes laid out as subdivisions of a larger permanent 
plot. The sizes of these plots are in proportion to the intensive ness of 
the problem and the age of the tunber. For determining the conditions 
which affect germination, plots from "10 to 20 feet square are large 
enough. On these plots every seedling is counted and sometimes each 
is marked by inserting a pin on which a tag can be attached. In this 
way the mortality and survival of the seedlings can be later ascertained. 
For the study of the development of reproduction, larger plots, up to 
1 acre in size, are required. On such plots there is no effort to keep 

1 Some New Aspects Respecting the Use of the Forest Service Hypsometer, 
Herman Krauch. Jom-nal of Forestry, Vol. XVI, No. 7, p. 772. 

Comparative Tests of the Klaussner and Forest Service Hypsometer, D. K. 
Noyes, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 417. 



314 IMPROVING THE ACCURACY OF TIMBER ESTIMATES 

a history of each individual tree, but the total number of trees in each 
class is recorded in height classes as follows: 

Overtopped =|' in height; 
i' = 2' in height; 
2' = 4' in height; 
4'= 1" in diameter. 
Free, same classes. 

By inch classes, 1, 2 and 3 inches. In these inch classes 
the trees are recorded in five crown classes: x, d, c, i, 
and s previously indicated. 

References 

" Average Log " Cruise, W. J. Ward, Forestry Quarterly, Vol. V, 1907, p. 268. 
Errors in Estimating Timber, Louis Margolin, Forestry Quarterly, Vol. XII, 1914, 

p. 167. 
A Method of Timber Estimating, Clyde Leavitt, Forestry Quarterly, Vol. II, 1904, 

p. 161. 
Forest Mapping and Timber Estimating as Developed in Maryland, F. W. Besley, 

Proc. Soc. Am. Foresters, Vol. IV, 1909, p. 196. 
An Efficient System for Computing Timber Estimates, C. E. Dunstan, C. R. Gaffey, 

Forestry Quarterly, Vol. XIV, 1916, p. 1. 
Timber Estimating in the Southern Appalachians, R. C. Hall, Journal of Forestry, 

Vol. XV, 1917, p. 311. 
Some Problems in Appalachian Timber Appraisal, W. W. Ashe, Journal of Forestry, 

Vol. XV, 1917, p. 322. 
Determining the Quality of Standing Timber, Swift Berry, Journal of Forestry, 

Vol. XV, 1917, p. 438. 

Reviews 

Error of Strip Survey (Sweden), Journal of Forestry, Vol. XVI, 1918, p. 938. 

Estimating for Yield Regulation, Schubert, Forestry Quarterly, Vol. XIII, 1915, 
p. 399. 

European Methods of Estimating Compared for Accuracy, Forestry Quarterly, 
Vol. XIV, 1916, p. 521. 

Volume Tables and Felling Results, Forestry Quarterly, Vol. IX, 1911, p. 632. 

Results of Errors in Measuring, Schiffel, Forestry Quarterly, Vol. IX, 1911, p. 628. 

Methods of Estimating Compared, Prof. Zoltan Fekete (Hungary), Forestry Quar- 
terly, Vol. XIV, 1916, p. 521. 

A New Method of Cubing Standing Timber (Hungary), Forestry Quarterly, Vol. 
XII, 1914, p. 474. 



PART III 

THE GROWTH OF TIMBER 



CHAPTER XXII 
PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

244. Purpose and Character of Growth Studies. The growth of 
timber is studied in order to determine the rate of annual production 
of wood as a crop on forest land. The yield of farm products is annual 
and is measured at harvest. The essential difference between farm 
and wood crops is that the period required to produce the latter is many- 
years in extent, and due to this fact forest land is not the only capital 
involved in crop production. The growth which the trees lay on 
annually becomes in turn part of the capital to which future growth 
is added in the same manner as interest which is added to a savings 
account. 

This increase in total volume of a stand of timber does not continue 
indefinitely, but only up to a certain age, which marks the culmination 
of growth of the stand, from which time the losses occurring in the stand 
more than counterbalance growth, and its volume and value diminish. 
Forest crops therefore mature as do annual crops and one of the pur- 
poses of growth study is to determine the period required for maturity. 

The basic facts to be determined in the study of growth are, first, 
the total yield of stands in terms of quantity of products, quality, and 
money value, for the period required to grow a crop of timber from 
origin to maturity; second, the average annual rate of growth to which 
this final yield is equivalent, which is termed the mean annual growth 
and is comparable to sunple interest on land as capital or to annual 
crops; third, the actual growth or increase in volume, quality, or value, 
laid on during definite periods in the growth of the stand. The growth 
for these short periods is expressed either as current annual growth which 
is the growth for a single year, -periodic annual growth which is the aver- 
age annual growth for a short period, or periodic growth which is the 

315 



316 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

total growth for the short period. The length of these periods is com- 
monly a decade, but may be from 5 to 40 years. The term current 
annual growth is commonly used in place of the term periodic annual 
growth, as indicating the average annual growth for a short period 
instead of the separate growth for a single year, though this use of the 
term is technically incorrect. 

Finally, the relation which the increase in volume or growth bears 
to the volume of the tree or stand on which it is produced may be 
expressed as growth per cent, and indicates the rate of increase with 
relation to the wood capital required for its production. This growth 
per cent may ho comput(Hl for volume alone, for growth in (quality of 
wood, or for growth in the unit price of the pi-oduct (§ 334). A growth 
per cent figure is not an index of absolute increase in either volume, 
quality or price, since it is merely the exioression of a relation between 
capital and increment existing at a given time. Growth per cent is 
usually based upon a single year's growth, either current or average 
for a period. One year's growth is seldom measured, since a decade, 
or at a minimum, a five-year period is I'equired to eliminate variable 
factors affecting a single season's growth caused by climatic conditions. 
Hence periodic annual growth is commonly substituted for current 
annual growth as a basis for computing growth per c?nt. 

245. Relation between Current and Mean Annual Growth. Growth 
may be studied either for an individual tree or for a stand, exi)ressed in 
terms of growth per acre. In either case, the current annual growth 
in volume increases at first slowly and then more rapidly to a maximum, 
after which it begins to decline and finally ceases with the death of the 
tree or the beginning of actual decadence of the stand. The sum of the 
current annual growths laid on foi- the entire period gives the total 
growth. The total growth or volume divided by the age in years 
gives the mean annual gi-owth (Fig. 64). 

The mean annual growth is an average rate of growth representing 
the total growth or yield at a given age, distributed or spread over this 
period. The actual productiveness of the forest is in this way compared 
with annual crops, which basis is otherwise obscured by the varying 
rate or curve of growth in volume of the trees from decade to 
decade. 

The mean annual growth at any given year is this average of past 
production. Current growth for the year or decade tends to increase 
constantly up to a given maximum. During this period the volume 
added each year to the total volume of the stand is greater than the 
average or mean annual growth up to that year. Hence this average 
is raised and the curve of mean annual growth increases. But it can- 
not increase at as rapid a rate as the current growth curve, since the 



CURRENT AND MEAN ANNUAL GROWTH 



317 



effect of this increase for the year upon the average increase is spread 
over all previous years. • 

When the current annual growth curve reaches its culmination and 
begins to decline, the successive average or mean annual growth figures 
for each year still continue to increase in spite of this fact, since the 
amount of growth added to the stand during the year although less 
than formerly is still greater than the average or mean. 

When the current growth for the year finally falls to an amount 
equal to the average or mean for the entire crop period, the curve of 
mean annual growth has reached its highest point. During the follow- 



180 



160 



140 



§5120 
SlOO 



.5 80 
2 
.■5 60 

>> 

40 
20 



5 10 15 20 25 30 36 40 45 50 55 60 65 70 
Age in Yeara 

Fig. 64. — Current and mean annual growth of a normal stand. 
Jack Pine Minnesota. 















r 


K 


























\/ 


\ 
























J 




\ 






















e 


y 






\ 




















a/ 








\ 


Year 
Mea 


of Cul 
1 Add 


ninati 
al Gr< 


on of 

iWth 












1 




JS>^ 




-Vu~ 












^ 


H - 








c 




M 


f 






^ 
















/ 


-Vi 


f 
















. 








^ 


"V 





















ing and subsequent years the current growth laid on is less than this 

mean, hence this average or mean begins to drop, but only to the extent 

that it is pulled down by the effect of this lesser current annual growth 

« . , XT- r X- total volume ^t 1 c- 

tor single years upon the traction, ■. . Hence as before, 

age m years 

this mean growth curve falls more slowly than the current growth 

curve. Unless these stands are cut, losses in the stand will finally 

exceed the growth, and the current growth curve would then become 

negative. But until the entire stand is destroyed, the curve of mean 

annual growth will still be positive. When properly computed on the 

basis not merely of volume, but of quality and price increment as well, 

the year of culmination of mean annual growth, rather than the current 

growth data, indicates the maturity of a stand and the age at which, 

if cut, it will produce the greatest average yields, when the period of 

production is taken into account. 



318 



PRINCIPLES UNDERLYING THE STUDY OF GROWTH 



246. The Character of Growth Per Cent. The growth per cent of 
a tree or stand cannot be compared with the per cent of interest earned 
annually on a fixed capital, since this growth is not separable from 
the wood capital on which it is laid, and thus causes this capital or base 
volume to increase annually. To maintain the same rate of growth 
per cent on this increasing volume, the amount of the annual growth 
must continue to increase at a geometric rate. Although the increase 
in volume of a stand during the period of most rapid current growth 
for a time does approach a geometric rate when compared to a given 
or fixed initial volume, yet even here the effect of the constantly and rapidly 
increasing volume of accumulated ivood capital upon the current annual 
rate of increase will cause this rate of growth per cent to drop consistently 
throughout the entire life of a tree or stand. The actual behavior of 
the growth per cent of a stand is shown by the following table: 

TABLE XLVII 
Growth of Jack Pine, Minnesota * 



Age. 


Yield per acre. 


Periodic 


Mean 


Periodic 






annual growth. 


annual growth. 


annual growth. 


Years 


Cubic feet 


Cubic feet 


Cubic feet 


Per cent 


20 


160 




8 


24.20 


25 


6.50 


98 


26 


14.12 


30 


1360 


142 


45 


9.52 


35 


2210 


170 


63 


4.68 
2.40 


40 


2800 


118 


70 


45 


3160 


72 


70 


1.56 


50 


3420 


52 


68 


1.24 


55 


3640 


44 


66 


1.08 


60 


3840 


40 


• 64 


0.88 


65 


4010 


34 


62 


0.80 


70 


4180 


34 


60 





* From Bui. 820, U. S. Dep. Agr., 1920, Table 10, p. 14. 

247. The Law of Diminishing Numbers as Affecting the Growth 
of Trees and Stands. The growth in volume of individual trees tends 
at first to follow a rate of geometric increase. Were the diameter growth 
of trees to remain uniform for a long period, a condition characteristic 
of many species, notably white and sugar pine, the resultant area and 
volume growth would increase at a ratio similar to that of D^, rather 
than D (§ 270). This rate of volume growth is strengthened by height 
growth. With maturity, the height growth of trees falls to insignificant 
proportions and the diameter growth of many species falls off to a marked 
extent. The result is a flattening out of the curve of volume growth, 



LAW OF DIMINISHING NUMBERS 



319 



which would otherwise continue to ascend sharply. This influence 
of age and maturity upon individual trees which survive is due to loss 
of vitality, but the same effect is observed in all the remaining trees 
which are suppressed during the growth of the stand and ultimately 
die because the space needed for their normal expansion is appropriated 
by more vigorous trees. 

A forest or stand represents an area of land stocked with trees. 
The number of trees which can grow and thrive upon the acre is in 
inverse ratio to the size of crown spread- and space required by the 
individual tree. As trees increase in size their numbers will be reduced. 
The enormous number of seedlings which may spring up on an acre 
is merely a guarantee that a few will survive to maturity. The curve 
of diminishing numbers which 
is characteristic of all species 
and classes of timber, drops 
very rapidly in the first few 
years, and more gradually later 
on. Numbers diminish most 
rapidly during the period of 
rapid height growth and crown 
expansion. When trees have 
reached their mature heights, 
their numbers have been re- 
duced to a point where the 
further diminution is a much 
slower process. 

The cause of reduction is 
at first failure to survive the 
juvenile period because of un- 
favorable climatic or soil factors 

and competition with other vegetation, followed by suppression due 
to the competition of older trees or of trees of the same age which have 
attained dominance by some advantage at the start. The crown is 
restricted in size and spread, is finally overtopped, and the tree dies. 

This process is accompanied by a change in the rate of diameter 
growth for the trees whose crowns and growing space are restricted 
in the struggle. Consequently the dominant trees maintain at all 
times the most rapid rate of diameter and volume growth, while others 
which at a given period have not yet lost their dominance and still 
show a rapid rate of growth, will later on, with the closing of the crowns 
and crowding of the tree, show a falling off in growth, sometimes quite 
sudden in character. The prediction of the future growth of any single 
tree is therefore impossible without knowing whether the tree will main- 



















































2000 
^1750 
1^1500 
|l250 

t!iooo 

o 

1 750 

i 500 
Z 
250 


























\ 






















\ 


s 






















\ 
























\ 






















\ 
























\ 
























■\ 


^ 










1 




















- 



10 20 30 



40 50 60 70 
Age, years 



80 90 100 



Fig. 65. — Number of trees per acre at dif- 
ferent ages in fully stocked stands of 
white pine. From Table XLVIII. 



320 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

tain its position in the stand and subdue its competitors. The net 
growth on an acre is the sum of the growth of the surviving trees. 

At any given period or year in the hfe of a stand, the number of 
trees is considerably less than were present and living at any previous 
period or decade, and is considerably greater than the number which 
will be alive at any given period or decade in the future. This loss in 
numbers, accompanied by rapidly lessening rates of growth of a portion 
of the surviving trees, plus the normal growth of the remainder, produces 
the net result or increase in the stand for the period, and any method 
of study of growth which does not take this natural loss and change 
into account will be inefTectual in predicting or measuring the growth 
of forests or stands. 

248. Yields, Definition and Purpose of Study. The past growth 
of the surviving portion of stands is represented by their present volume, 
the measurement of which is dealt with in Part II. This present 
volume represents the yield of the area, provided nothing has pre- 
viously been removed as thinnings or otherwise. But without a knowl- 
edge of the period required to produce this volume, the word yield is 
meaningless as it cannot be expressed in terms of the rate of produc- 
tion per year or mean annual growth. An estimate of standing timber 
is merely a statement of the volume at present found on the area. A 
yield, on the other hand, is a statement of the volumes produced on 
the area within a definite period of tittie. If the total volume is to be 
expressed as a yield, then the total age of the stand must also be known. 
If the yield for a shorter period, such as a decade, is to be stated, then 
only that portion of the volume of the standing timber must be shown 
as was laid on during this period. Otherwise, the rate of growth per 
year is not indicated. 

The growth of forests is studied primarily for the purpose of pre- 
dicting future growth on forest land. On the basis of past records of 
growth of trees and stands as shown by measurements of present 
attained volumes and of age, predictions can be made as to the future 
growth of these and of similar stands. 

This application or prediction may be made in one of two ways: 

1. B}^ projecting the rate of growth of an existing stand into the 
future. This is done either by assuming that the rate shown in the 
immediate past will continue imchanged in the immediate future, or 
else that this rate will change and that this tendency of future growth 
may be predicted by the shape of the past growth curve. Of these 
two assumptions the second is apparently the more accurate, but in 
neither case is it possible to predict the growth for more than a short 
period. 

2. Some better method of prediction is required to cover longer 



YIELD TABLES 



321 



periods and to determine the probable yield of crops of timber, the 
production of which is the purpose of forestry. This is accomplished 
by the second general method of prediction which rests on the principle 
of comparison. The past growth of existing stands is taken as an indi- 
cation of the expected future growth of other younger stands whose 
prediction is desired for a similar period. It is assumed that similar 
stands will grow in a similar manner. The task consists of demon- 
strating the relation between the stands whose past growth is measured 
and those whose future growth is sought. 

249. Yield Tables. The most practical and useful expression of 
growth is a yield table which shows the yields per acre for even-aged 
stands at different ages by five- or ten-year periods separated into 
different qualities of site. An example of such a yield table is shown 
below : 

TABLE XLVIII 

Yield Table for White Pine * 
Quahty II f 





Average 


Diameter 


Number 


Basal 


Total Yield 




height 
of 


breast- 
high of 


of 
trees 


area 
per 






Age. 








dominant 


average 


per 


acre 








trees. 


tree. 


acre 




Cubic feet 


Board feet 


Years 


Feet 


. Inches 




Square feet 






10 


6.0 


1.4 


2015 


20 


650 




15 


12.0 


2.2 


1834 


50 


1,150 




20 


19.5 


3.2 


1626 


90 


1,750 




25 


28.0 


4.1 


1420 


131 


2,420 


5,400 


30 


36.5 


•5.1 


1192 


169 


3,250 


9,600 


35 


44.5 


6.1 


950 


193 


4,180 


15,900 


40 


51.5 


7 1 


760 


209 


5,130 


23,500 


45 


58.0 


8.0 


633 


221 


6,100 


30,600 


50 


64.0 


8.9 


537 


232 


7,000 


36,600 


55 


69.5 


9.8 


460 


241 


7,800 


42,000 


60 


74.5 


10.7 


397 


248 


8,500 


46,900 


65 


79.0 


11.6 


348 


255 


9,200 


51,600 


70 


83.0 


12.4 


311 


261 


9,840 


56,100 


75 


86.5 


13.3 


277 


267 


10,400 


60,200 


80 


90.0 


14.1 


251 


272 


10,930 


64,000 


85 


93.0 


14.9 


229 


277 


11,400 


67,500 


90 


95.5 


15.7 


210 


282 


11,850 


70,900 


95 


98.0 


16.4 


195 


286 


12,250 


74,000 


100 


100.0 


17.1 


182 


290 


12,630 


77,000 



* Taken from Tables 4 and 6 in " White Pine under Forest Management," U. S. Dept. Agr. 
Bui. 13, Washington, 1914, pp. 22 and 23. 

t Similar tables are prepared for Qualities I and III. 



322 



PRINCIPLES UNDERLYING THE STUDY OF GROWTH 



From the above table, the periodic growth for separate five-year 
periods may easily be obtained by subtracting the volume at one age 
from that of the succeeding period. 

250. The Application of Yield Tables in Predicting Yields. An 
example of the prediction of volume growth in existing stands of timber, 
on the basis of periodic growth by decades is given in the following 
table which shows the present yield of timber over 10 inches and the 
future yield which may be realized upon the timber left standing below 
this diameter limit, and not shown in the table. 



TABLE XLIX 

Yield per Acre of Spruce Cutting to Various Diameter Limits * 

Based on stands containing approximately 5000 feet B.M. of timber 10 inches 
and over in D.B.II. per acre 





Am't 


Second Cut 


Second Cut 


Second Cut 






of first 


after Ten 


AFTER Twen- 


after Thir- 






cut. 


Years 


ty Years 


ty Years 


Interval 
required 


















between 






Num- 




Num- 




Num- 




equal 






ber of 




ber of 




ber of 




cuts 




Board 


mer- 


Board 


mer- 


Board 


mer- 


Board 


in 




feet 


chant- 
able 
trees 


feet 


chant- 
able 
trees 


feet 


chant- 
able 
trees 


feet 


years 


Cutting to a 10-inch limit 


5213 


7.3 


365 


16.2 


1087 


26.8 


2483 


43 


Cutting to a 12-inch limit 


4341 


14.3 


1208 


21.6 


2325 


30.5 


4109 


32 


Cutting to a 14-inch limit 


3382 


10.3 


1470 


16.8 


3044 


40.8 


6351 


21 



* Compiled from Yield Tables in " Practical Forestry in the Adirondacks," Bui. 26, Division 
of Forestry, U. S. Dept. Agr., 1899, pp. S3 and 84. 

To understand the use or application of a yield table in predicting 
growth, it must be realized that the stand or rate of growth upon a 
given acre or tract will seldom if ever exactly agree with that shown in 
a yield table even when these yields are separated by qualities into 
3, 4 or 5 classes of site. In the case of bare land or very young timber, 
this probable difference may be ignored, the site regarded as equivalent 
to one of the site classes given and the yield predicted as if it would 
coincide with that of the table. But for most stands which have already 
reached a considerable age and the prediction of whose further growth 
is desired, a comparison with the yield table should give a more exact 
prediction of the growth of the stand in question. The yield table in 



PREDICTION OF GROWTH 



323 



this case, instead of predicting exact future growth, is used as a standard 
to express the relative increase or decrease in the yield or stand per acre. 
The yields may be plotted and will form curves of growth in volume 
per acre. The yield of any stand whose present volume and age are 
known represents a definite per cent of some existing yield from this 
table. The growth of this stand may be predicted by using the same 
per cent of the values in the table for the future. 

In Fig. G6 the present yield of a plot of white pine of fifty years is 
indicated and the basis of prediction for its future yield is shown. 
This percentage relation based upon standard yield tables is exten- 
sively applied in forestry to obtain the actual yields of large forest 

L0.O00 

9,000 
« 8,000 
"!? 7,000 
,000 



I* 

o 
13 

1, 



,000 
,000 
,000 
,000 
,000 




















^ 


QualiyI 
















^ 


^.. 


.--'' 


< 

Quali 


,., 












/ 


y 


*1-^ 




.J 














/ 


/ 


y 


^j 


'-^ 




Quali 


ylll 








/ 


/ 


y 




^ 
















/] 


/) 


iy^ 


















A 


/ 


/ 








Plot X at 60 
92 !i of Qual 
The yieia at 


years yields 
ty I standar 
65 years is 


d. 




// 


7 










predicted as 
standard at 
For Plot o 


92^ <^f the 
that age. 
Jie reliction is 




// 












10b 5t 
10 ye 


of Qu. 
rs 


lity i: 


I at 






/ 























25 30 35 40 



45 50 55 60 
Age in Years 



65 



Fig. 66. — Method of predicting yields of specific stands by comparison with standard 
curves of yield for different qualities of site. White Pine, Mass. 



areas. It is the basic idea underlying the prediction of growth by 
the method of comparison. 

251. Prediction of Growth by Projecting the Past Growth of Trees 
into the Future. By either of these methods, comparison or projec- 
tion, it is assumed that no records exist of the past condition of the 
stands whose growth is to be found. Their present volume, and the 
age and past growth in diameter, height and volume oj the trees now 
standing can be studied, but there is no reliable indication of the 
number of trees lost during the past period, though evidences remain 
for a time in the form of dead and down trees.^ 

1 The writer once noticed in a densely stocked stand, the stems of hundreds of 
small lodgepole pine which had fallen across a tamarack log and been preserved from 
decay, when all trace of similar dead trees on the forest floor had disappeared. 



324 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

In using the past growth of a stand on which to base the prediction 
of its future growth, these records of past growth of the Hving trees 
in diameter, height and volume are the only data available. This 
prediction is based on one of two assumptions, either that the growth 
for a future period will continue at the sayne rate as shown for a past 
period, or that this future growth will be at a different rate, either increas- 
ing or decreasing, and that the amount of this change may be deter- 
mined by a study of past growth. 

In the use of either of these methods to predict the growth of trees, 
the method may be applied either to the volume of the tree or to its 
diameter and height instead. If a volume analysis is made for two 
or more past decades, it may be assumed either that this rate of volume 
growth will continue unchanged, an assumption which is practically 
never correct, or that the curve of volume growth which may be plotted 
from past volumes can be prolonged to indicate the growth of the next 
decade. 

But the method more commonly employed is to substitute a study 
of diameter and height growth for volume analysis. If future diameter 
growth is assumed to be at the rate shown in the past decade, future 
volume growth will increase (§ 270). If the past growth in diameter 
is plotted, and a curve projected, the future diameter so obtained is 
the basis of the predictetl growth in volume. 

252. The Effect of Losses versus Thinnings upon Yields. The 
first conception in the study of growth is apt to be that it consists chiefly 
of measuring the growth in diameter, height and volume of individual 
trees. Although it is true that growth per acre is based primarily upon 
the rate of growth of the individual trees which make up the stand 
and that according as this rate of tree growth is rapid or slow, the yield 
per acre will be large or small, yet the total growth per acre, which is 
the result desired in all growth studies, is the product of the growth 
of individual trees and the number of trees surviving to the end of a 
future period plus such growth as may take place on trees which die 
and are removed during the period. The death of a certain number of 
trees in the stand during the period will have this effect, that if these 
trees can be removed as thinnings, their volume at the beginning of the 
period, augmented slightly by growth which takes place in them before 
they die, is part of the yield for the period, but does not appear in the 
volume of the standing timber alive at its end. If these trees cannot 
be harvested, their total volume as originally measured will disappear 
from the live stand, and constitute a negative growth or loss which 
must be deducted from the groivth on the surviving trees before the actual 
volume of the stand at the end of the period can be correctly ascertained 
from its volume at the beginning. 



AGE IN EVEN-AGED VERSUS MANY-AGED STANDS 325 

This problem may be illustrated as follows: 

A stand of pine has now 10,000 board feet per acre. The growth for ten years 
upon the trees which will survive will be 4000 board feet. The trees which will die 
in ten years have now a volume of 1500 board feet. This means, first, that the 
growth of 4000 board feet is actually put upon a present volume of 8500 board feet; 
second, that the remaining 1500 board feet must either be included in or deducted 
from the final yield, on the basis of whether it is actually salvaged or not. There 
may have been some growth on these trees, but this can be neglected. On the assump- 
tion that no cutting of thinnings is possible, the net yield on this acre at the end of 
the decade is 12,500 board feet. If thinnings are harvested, the yield is 14,000 board 
feet. Had the growth prediction been attempted by measuring the growth of indi- 
vidual trees, those representing the 1500 board feet would have to be excluded from 
the calculation of total growth in either case. Unless salvaged, they represent an 
actual negative growth reducing the net gain by 1500 board feet. 

Unless it is possible to guess just how many and which trees are 
going to die, not only the volume, but the growth for ten years on some 
of these trees will probably be erroneously, included, instead of being 
subtracted from the predicted total yield in ten years. The possible 
error in subtracting either too few or too many trees is very large 
since the size of the error is doubled for stands when thinnings are 
impractical. It is obvious that a method depending instead on direct 
measurement of the result at the end of the period on older stands 
and the comparison of such measurements with similar younger stands 
furnishes a. safer basis of growth predictions on these younger stands 
for any considerable period than efforts to project into the next period 
the rate of growth of the trees now standing. 

Where stands are under intensive management, the trees which 
will die are thinned out, probably at the beginning of the period, and 
utilized. The loss for the succeeding ten-year period is then exceedingly 
small unless accidental im*oads occur from wind, insects or other destruc- 
tive agencies not anticipated. It is therefore safer to predict growth 
for short periods on stands which have been under management and 
have been thinned than it is on stands where thinnings and utilization 
of the dying material is impossible. 

253. The Factor of Age in Even-aged versus Many-aged Stands. 
Where stands are measured as a unit to determine the production per 
acre, three factors are needed: first, the present volume of the stand; 
second, its average age or the time which it took to produce this volume; 
third, the area which it occupies. The age of the stand as a whole 
is desired. If the stand is even-aged it is sufficient to determine merely 
the age of one of the trees adequately to measure the period of pro- 
duction and the rate per year. This can be done by counting the annual 
rings of growth without any measurement whatever, on the assumption 
that the species has formed but one annual ring per year. This premise 
does not always hold good, since with certain species in certain localities, 



326 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

false rings may be formed, giving two rings per season (§ 256). Pro- 
vided age can be determined, the study of diameter, height and volume 
growth of individual trees is entirely unnecessaiy for even-aged stands, 
as a means of determining the yields per acre. 

But where stands are composed of trees of different ages on the 
same area, it becomes practically impossible to determine the average 
age of the stand by any such direct method. Within certain limits, 
that is, if the ages of the trees composing the stand do not vary too 
greatly, it is possible to determine an age which may be accepted as 
the average period required to produce the present volume. Where 
the diversity of age is so great that this is impossible, it is necessary 
to shift the basis of age determination from the mere counting of the 
rings to a determination of the age of trees of a given size or diameter. 
To determine ages, trees must be cut down or the center reached by 
borings or choppings. While possible on one or two trees, it becomes 
out of the question to test every tree in this manner without cutting 
down the stand. Diameter, on the other hand, can be readily measured. 
For stands of mixed ages, therefore, two methods are possible. By 
the first, the average diameter of the trees in the stand is found, and the 
age of a tree of this size is determined and is assumed to indicate the 
average age of the stand. By the second, no attempt is made to 
determine the age of the stand, but instead the growth may be studied 
for trees of given diameters, and for a short current period, past and 
future. Either method requires the measurement of the diameter 
growth of trees to determine the number of years or period which is 
required to produce trees of given sizes or to grow 1 inch in diameter. 

254. The Tree or Stem Analysis and the Limitations of its Use. 
The volume growth of an individual tree may be analyzed with almost 
absolute accuracy by cross-sectioning the bole and measuring the width 
of the annual rings at different sections by decades. This is termed 
stem analysis, or tree analysis. The accuracy of these results for a single 
tree is apt to create a false impression in the minds of investigators 
as to the value of the figures thus obtained. To what use will volume 
or total tree analyses of growth of trees be put? What question will 
they answer? Will they predict the growth per acre of stands or the 
rate of growth per year on an acre of land? The cost of a tree analysis 
is excessive compared with the direct measurements of yields and 
total age or even the measurement of diameter growth on the stump. 
The number of trees which may be analyzed is therefore limited. How 
shall these trees be selected? It has been seen in the study of volume 
tables that trees vary quite extensively in form. To get average 
growth we must be sure of obtaining average form. Average form is 
best obtained by averaging hundreds of trees as is done in the prepa- 



CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 327 

ration of volume tables, but the few trees analyzed for growth may- 
be either cylindrical or neiloidal in form. We therefore may have a 
perfect record of the past growth of certain selected trees which vary 
in form and volume at least 10 per cent from the average desired. 

Even if this difficulty can be overcome by careful selection of trees 
of average form quotient, and a few of these average trees analyzed 
for past growth, how are these past results to be applied in predicting 
future growth? It is evident that the growth of individual trees is 
only a part of the problem, for the average tree in a well-stocked stand 
at a given age does not remain the average tree for future periods and 
was not the average tree at any period in the past. The trees which 
die in a stand are naturally the smaller, more suppressed specimens 
with the smallest diameters. In the lapse of a ten-year period, the 
loss of a number of trees from the lower diameter classes will raise the 
average diameter and volume of the remaining trees so that the tree 
which is now the average is in ten years dropped into a class below the 
average. 

There is but one way of even approximating the growth of a stand 
in the future by means of the analysis of volume growth of individual 
trees. If the number of trees which will probably survive to a given 
age can be predicted (which can best be ascertained by the method 
of comparison and yield tables), the selection of this number from a 
younger stand, taking trees wholly in the dominant class, will indicate 
the character of tree which must be cut and measured to determine 
the growth for the future. Yet even here it is better to take a tree 
which is fully mature and shows the growth for the entire period, in 
which case the stand, rather than the tree, is the better unit. 

255. Relative Utility of Different Classes of Growth Data, and 
Chart of Growth Studies. To sum up these principles: past growth 
is measured in order to predict future growth. Growth on an area 
and not the growth of single trees is wanted. The three essentials 
of growth are volume, time and area. For even-aged stands the time 
element is the total age and may be determined by counting rings on 
one or two sample trees. This requires a minimum of investigation 
in addition to volume measurements. 

Diameter growth of trees comes next in importance and is used 
when size must be depended upon to determine age either for the total 
period or for shorter current periods of growth when diameter is sub- 
stituted for age. 

Height growth of trees comes third in importance since it is used 
to indicate site quality (§ 296). It may also be used together with 
diameter growth, to predict the volume growth of trees by a method 
much shorter than volume analysis (§ 288). 



328 



PRINCIPLES UNDERLYING THE STUDY OF GROWTH 



Volume-growth analysis of individual trees, although apparently 
the most accurate and scientific basis of growth, is in reality the least 
important and most inefficient when expense is compared with results. 
It is invaluable to determine the laws of tree growth and the changes 
which may take place in the form of individual trees as the result 
of changed conditions, as for instance, on cutover lands, and as a pre- 
caution against accepting general figures based on volume tables and 
other short methods of growth study. But ordinarily, even where 
volume of trees is desired, it will be obtained from diameter and height 
growth supplemented by use of the form quotient rather than from 
the stem analyses of trees. Many thousands of stem analyses have 
been made in the past whose results were either not worked up at all 
or since compilation have reposed in the archives of Government and 
States while investigators vainly sought an answer to the pressing 
problems as to what was the actual rate of growth per year on national, 
state and private forests. 

The best possible basis for growth predictions is the actual records 
of the growth in successive periods of specific forest stands whose 
history is known and whose conditions of management are fixed. The 
establishment of sample areas which are measured successively by 
ten-year periods will give a firm basis for growth predictions superior 
either to the method of comparison, based on past growth of older 



Chart of 



Purpose of growth study § 244 



Basis 



Field measurements 



I Normal or index yields 

Productive capacity of different qualities of forest per acre for even-aged 



land— § 303 







II 


Prediction of 




For even-aged stands 


f u t u r e 




— §§ 256-262 


growth and 






yi e 1 d s on 






natural 


For total age 




forest areas 


or long per- 




—§§247- 


iods — 




248 


§§249-250 





stands 

1. Pure stands— § 304 1. Diameters B.H.— 
§ 309 

2. Mixed stands — § 314 2. Heights, total 

3. Count of annual rings 
on average trees — 
§262 



Comparison of stands 1. Timber estimate sepa- 
with normal yields at rated by age classes — 
same age — § 301 § 344 



Counts of annual rings 
on average trees — 
§ 262 



CLASSES OF GROWTH DATA, CHART GRQ^'TH STUDIES 329 

stands, or to the effort to predict the growth of stands from that of 
the trees which they contain. As a result of similar actual records 
of production the working plans for some European forests dispose of 
the subject of growth quickly, stating substantially that the growth 
in this class of forest is known, from past records covering (perhaps) 
200 years, to be about so much. 

In the chart, on pages 328-333, eleven main lines of investigation 
of growth are listed, as a guide to the discussions in the following chap- 
ters. The object of a study should first be understood, and the con- 
dition of the stands to which it is to be applied, as indicated in the 
three columns under " Purpose of Growth Study." In the column 
under " Basis " the principles on which the solution of the problem 
depends are outlined. 

The remaining columns are seK-explanatory. Column 6 shows the steps 
by which the study can be applied to large areas of forest land, thus secur- 
ing the data for which the preceding steps are merely preliminary. 

By using this chart as a guide, and consulting the references to 
discussions of principles and methods, under each step, one may hold 
the purpose of growth studies clearly in mind and choose the best 
method of accomplishing the desired object. 

The relative importance and relial)ility of the methods given are 
indicated by the quality of type used in the table. 

rRowTH Studies 



Offif 



)rds 



Final data olitained 



Application to forest 
areas 



Data derived from the 
investigation 



Area of sample plots- 

§ 308 

Volumes of trees (vol 

ume tables) — § 131 

Age of sample trees- 

§ 255, § 257 

Height of dominant 

trees— § 310, § 311, 

§312 



1. Volume per acre — 
§ 306 

2. Age of stands — § 256 

3. Height of stands 



Classification of site qual- 
ities—! 294, § 345 

1. On basis of height 
growth — §§ 296-310 

2. On basis of volume 
growth—! 295, § 312 



1. Mean annual growth 
—§245 

2. Number of trees per 
acre 

3. Basal area per acre 

Maturity of stands — 
§ 244 (rotation) 
5. Maximum yields 



Area of stand or age 
class 



Volumes of trees (vol- 
ume tables )§ 131 

Age of sample trees — 
§ 256, § 257 
Average volume per 
acre for age class 



Reduction per cent or 
relative volume de- 
rived from this com- 
parison — § 317 
Empirical yield table 
based on this reduc- 
tion— §§ 304 316 j 



Empirical yield table to 
predict future growth 
on each age class 

Correction for i n - 
fluence of number of 
trees per acre at differ- 
ent ages— §§ 301-317 



Future yields based on 
actual stocking — 
§ 301, § 343 

Losses due to natural 
agencies — § 293 



Gains possible from 
protection and silvi- 
culture 



330 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

Chart of Growth 



Purpose of growth study 



Predict! on 
of future 
growth and 
yields on 
natural for- 
est areas — 
§§ 247-248 



III 

For large age groups- 
§ 318, § 321 



For total age 
or long per- 
iods — 
§§ 249-250 



1. Segregation of large 
age groups — § 320 



2. Comparison of group 
with normal yields at 
average age — § 301 



IV 

For many-aged stands 
§ 298. by diameter groups 
— § 323 



For many-aged stands based 
on crown spacers 298 



On thinned areas — § 326 



Basis 



1. Diameter groups substl 
tuted for age classes — § 270 
. Comparison of diameter 
group with normal yields at 
Indicated age — § 301 



1. Space required for develop 
ment of Individual trees— 
5 300 

2. Normal number of trees per 
acre at different ages — § 247 



Same as Va 



Field measurements 



1. Diameters B.H. 



2. Heights, average 
based on diameter 

3. Growth in diameter at 
stump, based on age of 
trees— §§ 265-269, 
§320 



1 . Diameters B.H. 



Heights 

Counts of annual rings on 
trees of each diameter class — 
§ 276 



1. Diameters of crowns based 
on D.B.H.— § 324 

2. Growth In diameter at stump 
based on age of trees — 
§§ 275-279 

3. Growth In height based on 
age— § 284 



Same as Va 

Mear-.ure only dominant trees — 
§ 263 



VI 

For even-aged stands 
— § 335 



Same as II 



Same as II 



Predic tio n 
o f future 
growth and 
yields on 
natural for- 
est areas — 
§§ 247-248 



YII 

For manv-aged stands 
§253, §299 



Past growth of existing 
trees — § 336 



For short 
periods or 
current 
growth — 
§§ 251-252 



Diameters B.H. by 
crown classes 



Heights, average 
based on diameter 



3. Growth in diameter at 

B.H. or stump 

— for given period of 
years — § 278 

— separated into 2 or 3 
periods of five to 
ten years — § 279 



CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 331 



Studies — Continued 



Office records 



Final data obtained 



Application to forest 
areas 



Data derived from the 
investigation 



1. Total number of mer- 
chantable trees 



2. Volumes of trees (vol- 
ume tables) (average, 
on diameter) 

3. Age as basis of each 
group, from normal 
yield table 

4. Diameter of tree of in- 
dicated age — § 275 

5. Volume of tree of indi 
cated diameter — § 278 

6. Number of trees in 
each age group — § 321 



1. Areas occupied by 
each of two age groups 
—§319 

2. Volumes in each age 
group — § 321 

3. Reduction per cent- 
§317 

4. Empirical yield table 
—§316 



Empirical yield table 
applied to area and 
age of each group — 
§ 322 and § 346 
Correction by segrega- 
tion of areas occu- 
pied by immature age 
classes— §§ 341 -348, 
§349 



Same as for II— § 301 



1. stand table by diameter 
classes — § 188 

2. Volumes of trees 

3. Average ags of trees of given 
diameters— § 276, § 323 



1. Areas occupied by each 
diameter group — § 319 

2. Volumes In each group 

3. Reduction per cent — § 317 

4. Empirical yield table — §316 



1. Empirical yield table ap 
piled to area of each diam- 
eter group 

2. Correction by segregation of 
areas occupied by Immature 
age classes — § 341, § 348. 
§ 350 



Results only approximate due 
to substitution of diameter 
for age 



1. Space occupied by circular 
crowns and resulting num 
ber per acre — § 324 

2. Relation between crown 
spread and diameter — 
§ 324 

3. Height and volume of trees 
of each diameter — § 288 

4. Average diameter of trees at 
each age — § 275 



Artificial normal yield table 
based on number and size of 
trees at each age — § 324 



Reduction per cent for appllca 
tlon of yield table deter 
mined by comparison of 
numbers of trees of each 
diameter on area with num- 
ber per acre In table — § 325 



Substitute for yields based on 
even-aged stands when latter 
cannot be obtained 



Same as Va 



Same as Va 



Same as Va 



Means of predicting yields of 
thinned stands 



Most accurate basis for 
current growth for 
short periods, on even- 
aged stands — § 327 

Growth per cent 



Same "s II 



Same as II 



Same as II 



1. Stand table by diam 
eter classes — § 188 



2. Growth in diameter 
and height of trees by 
diametter classes for 
past period — § 277 

3. Volumes of trees now 
and at end of period. 
From volume tables — 
§ 2SS. (Stem analyses 
only as a check on 
accuracy of 2 and 3) — 
§254 



Growth in volume of 
trees for future period 



2. Number and character 
of trees which will die 
during period — § 257 

3. Net volume growth for 
stand— § 252 



As applied to trees and 
stands 

1. Future growth of trees 
by comparison with 
growth attained by 
other larger trees for- 
merly of same diame- 
ter— § 278 

2. By extending into fu 
ture the past growth in 
diameter on trees 
whose future growth is 
sought 
— by assuming it to 

equal past growth 
— by prolonging curve 
based on past peri- 
odic diameter 
growth— § 279 



General method for cur- 
rent growth of stands 
of any character of 
stocking, form or ages, 
and mixture of species 
— §§ 24,5-342 

Growth per cent (§ 246) 
for trees or stands — 
This cannot in turn 
be substituted for 
growth measurements 
except on similar 
stands— §§ 331-333 

For stands whose age 
classes cannot be deter- 
mined 



332 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 

Chart of Growth 



Purpose of growth study 


Basis 


Field measurements 


1 






— for last inch or half- 






For many-aged stands 


Past growth of existing 


inch of radius — 


Prediction 




§ 253, § 299 


trees— § 336 


§278 


of future 


For short 






4. Growth in height 


growth and 


periods o r 






— by cutting back tip 


yields on 


current 






for required pe- 


natural for- 


growth — 






riod— § 294 


est areas — 


§§ 251-252 






— by substitution of 


§§ 247-248 








relation of height 
to diameter — 
§ 285 






VIII 


Past growth of trees for 


1, 2 and 4 same as VII 




For short 


For many-aged stands 


period since cutting, on 


3. Growjth in diameter 




periods — 


—§254 


formerly cut-over areas 


preferably at B.H.: for 




§336 




— § 286, § 336 


period since previous 
cutting. May be sepa- 
rated into five- or ten- 
year periods — §§ 278- 


Prediction oi 








280 


future 










growth and 










yields o n 










e u t V e r 










areas on 


For long periods 


IX 


1. Proportion of total area re- 


Same as III or IV— 5 320 


residual 


— § 338 


For even-aged, or 


maining stocked after cut- 




stands — 
§2S0 




large age groups or 
diameter groups 


ting, based on density equal 
to empirical yield tables for 






— § 339 


forest previous to cutting 










2. Residual area assumed to be 










clear cut 










3. Growth predicted for stocked 










area by empirical yield table 










—see II— § 316 





X 


Permanent sample plots 


1. 


Diameters B.H. with 


Historical record of growth per acre — § 326 


remeasured at stated 
intervals — § 243 




diameter tape — § 190 






2. 


Total heights, from 
fixed stations — § 199 






3. 


Crown classes and 
condition 






4. 


Plot description 






5. 


Tree fags and perma- 
nent boundary monu- 
ments 


XI 


Relation between diam- 


1. 


Diameters B.H. 


Effect of numerical density of stocking, and of thin- 


eter growth, crown 


2. 


Heights 


nings on growth of individual trees and on stand — 


classes and number of 


3. 


Growth in diameter 


§ 270, § 273, § 274 


trees per acre, from 




based on age, but rings 




sample plots — § 300 




counted inward, per- 
mitting study of cur- 
rent growth on same 
trees— §§ 265-269 



CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 333 
Studies — Continued 



Office records 



Final data obtained 



Application to forest 
areas 



Data derived from the 
investigation 



4. Tally of trees with 
suppressed crowns or 
those apt to die 



As applied to forest areas 

1. Stand table by diam- 
eter classes 

2. Growth from diam- 
eter and height 
growth and volume 
tables 

3. Correction for loss in 
numbers of trees 



Source of inaccuracy is in 
determining mortality 
per cent, hence cannot 
be applied to long 
periods 



1, 2, 3 and 4 same as VII 
5. Partial stem analyses 
for current growth in 
volume on sample 
trees as check on effect 
of increased growth at 
stump — § 290 



1. Probable growth in 
volume of trees left on 
cut-over areas 

2. Proportion of stand 

showing increased 
growth — § 337 

3. Loss in numbers and 
net growth in volume 



Future growth of trees 
by comparison with 
growth attained by 
trees on areas after cut- 
ting 
Growth on forest areas 
1, 2 and 3 same as VII 
4. Per cent of stand 
showing increased 
growth — § 337 



EfTects of 

— expansion of areas 
of crowns and in- 
creased growing 
space 

— c o m p e t i t i o n of 
species left after cut- 
ting 

— degree of severity of 
cutting on remaining 
stand 



Same as III or IV — § 321 



1. Areas In each age class lor 
timber left on cut-over area 



2. Volumes In each age class- 
§ 339 



Same as III or IV — § 322 



Minimum or conservative 

yields on cut-over areas 
No Increased growth assumed 

Conditions would coincide 

with cutting of even-aged 

stands 
Results contrasted with VIII 

as check on that method of 

prediction 
Safe for application to long 

periods 



1. Individual record of : 
each tree on plot by 
number, compared for 
successive measure- 
ments at five- or ten- 
year intervals 

2. Record of conditions 2. 
and of external in- 
fluences 



Permanent record of 
changes in volume, 
number of trees, and 
dimensions for plot 



Causes and extent of 
damage 



1. Location of plots with- 
in control strips on 
areas showing typical 
conditions to be 
studied 



Current growth, measure- 
ment of all factors of 
change in stands under 
conditions selected — 
§ 340 

Yield tables for stands 
grown under manage- 
ment. Ultimate solu- 
tion of all growth prob- 
lems — § 313 



Diameter growth for trees 
of separate classes, by 
diameters, and crowns 
— § 275, § 276, § 277 



Effect of spacing or thin 
ning upon volume 
growth and upon aver 
age sizes and quality of 
individual trees — § 301 



1. Stand tables by diam- 
eter classes 

2. Ages of stands. The 
data are applied inten- 
sively to individual 
stands in silviculture 



Proper spacing for plan- 
tations 

Character, and frequency 
of thinnings 

Class of material to grow 

Character of initial natu- 
ral stocking desired 

Growth per cent on stand- 
ing trees— § 330 



334 PRINCIPLES UNDERLYING THE STUDY OF GROWTH 



References 

Climatic Cycles and Tree Growth, A. E. Douglass, Carnegie Institute Pub. No. 289. 
Tree Growth and Climate in the United States. K. W. Woodward. Journal of 

Forestry, Vol. XV, 1917, p. 520. 
The Climatic Factor as Illustrated in Arid America, Ellsworth Huntington, Carnegie 

Institution of Washington, D. C, 1914, Chapter XII. 
Density of Stand and Rate of Growth of Arizona Yellow Pine as Influenced by 

Climatic Conditions, Forrest Shreve, Journal of Forestry, Vol. XV., 1917, p. 

695. 



CHAPTER XXIII 
DETERMINING THE AGE OF STANDS 

256. Determining the Age of Trees from Annual Rings on the Stump. 

The age of standing timber can only be determined from the ages of 
the trees which compose the stands. The age of a tree is the period 
elapsing from the germination of the seed or origin of the sprout to the 
present year. A record of the number of years of growth in a tree is 
made by the formation of the annual rings in which the light spring 
wood is sharply differentiated in color and texture from the heavier 
and darker band of summer wood of the year preceding. The count- 
ing of these annual rings determines the age of the tree. 

It is not always possible or easy to make this determination. Unless 
the growth of a tree is marked by annual seasonal changes, there are 
no annual rings to distinguish. This is true of most species of tropical 
woods, except those growing in regions marked by an annual cessation 
of growth due to annual recurrence of dry seasons. In some species 
of hardwoods there is such a slight difference between the texture of 
the spring and summer wood that the annual rings can be detected 
only with difficulty and by the aid of coloring matter and magnifying 
glass. This is true of such trees as basswood, hard maple and sweet 
gum. Many trees on dry sites grow so slowly that the annual rings 
are almost impossible to distinguish except by a glass. In counting 
rings it is usually necessary to smooth off the surface with a sharp knife 
or chisel in order to bring out the contrast. 

Where growth is affected by severe droughts, and sometimes where 
the trees are defoliated by insect attacks and later acquire new foliage, 
a false ring may be formed, giving two rings in a single year which 
would lead to an exaggeration in the age of the tree. This was found 
to be the case with Rocky Mountain juniper on dry sites. False 
rings may be detected if sufficient care is used, since they seldom form 
a complete circle, but are present on only a portion of the circum- 
ference and are therefore imperfect. 

The last annual ring of wood is not completed until after the growth 
for the year is finished. It must be distinguished from the ring of 
new bark laid down in the same season. The first two or three rings 
on some seedlings are difficult to distinguish. 

335 



336 



DETERMINING THE AGE OF STANDS 



The increment borer (§ 277) may be used to determine the age 
of standing trees at breast height or at any section accessible, provided 
the diameter is not too great and the position of the core of the tree 
can be found by the instrument. This method is used with such 
species as spruce. 

257. Correction for Age of Seedling below Stump Height. The 
number of rings in any cross section of a tree will indicate only the age 
of the tree at that cross section and not the total age. No rings can 
be formed at a given height above the ground until the tree reaches 
that height. The age of each cross section made in sectioning a tree 
will be less than that of the section below by just the number of years 
occupied in height growth between the two points. Although the 
total age of a tree can be determined theoretically bj^ taking a section 
even with the surface of the ground, this is seldom if ever done. The 
rings are counted at the stump, which gives the age of the tree minus 
the time which it took the seedling to reach this height. To get the 
true age of any tree, seedling ages based on height must be added to 
ring counts taken at stump heights. By cutting at the ground and 
counting the rings on a sufficient number of dominant seedlings which 
are sure to survive and therefore represent the average height growth 
of mature timber when at this age, a table is constructed showing the 
relation between the age of seedlings and different stump heights. In 
rapidly growing trees this makes from one to five years' difference 
in the total age, but with some species which have a long juvenile period, 
as much as twenty years may be required for a seedling to grow 2 feet 
in height. This is true of certain Western conifers. Hardwood sprouts 
on the other hand attain stump height in the first year. 

TABLE L 

Height of Seedlings at Different Ages, Western Yellow Pine, Colfax Co., 

New Mexico 



Age. 


Height. 


Age. 


Height. 


Years 


Feet 


Years 


Feet 


1 




7 


1.7 


2 


0.5 


8 


1.9 


3 


0.7 


9 


2.2 


4 


0.9 


10 


2.4 


5 


1.1 


11 


2.7 


6 


1.4 


12 


3.0 



♦Forest Tables — Western Yellow Pine. Circular 127, U. S. Forest Service, 1908. 



ANNUAL WHORLS OF BRANCHES AS AN INDICATION OF AGE 337 

The juvenile period for conifer seedlings is, as a rule, longer than 
that for hardwoods, though there are exceptions. Stump height may 
be separated into 6-inch height classes for determining the number of 
years to add for seedling heights to get total age of tree. 

258. Annual Whorls of Branches as an Indication of Age. There 
is another method, of very limited application, for determining the age 
of standing trees. This is applied to conifers and is confined to those 
species which form but one whorl of branches per year. Species like 
jack pine or loblolly pine, which form two or more whorls per year, 
cannot be judged in this manner. The approximate age of the tree 
and stand is obtained by counting the number of whorls. This record 
holds good only when the branches or dead stubs remain visible and 
when the height growth continues normal. The record is lost if all 
traces of the lower whorls are obliterated. If this is only for a height 
of from 5 to 10 feet, the average age of trees of this height may be 
obtc,ined from a study of seedling heights and used to supplement 
the remaining count. When the height growth of the tree has reached 
its maximum, a new whorl of branches is no longer formed annually, 
but the leader, as well as the branches, extends its growth by prolonging 
a single shoot. 

The ages of seedlings of many species may be determined by count- 
ing whorls of branches, or terminal bud scars if the whorls are not all 
there. In such cases it is not necessary to cut the seedlings and count 
rings. The bud scars are distinct for many years on species such as 
Douglas fir, Alpine fir, and others. 

259. Definition of Even-aged versus Many-aged Stands. The age 
of trees determines the age of stands. But unless it is known that 
the entire stand originated in a single year, as is the case with sprouts 
or with some species of conifers, such as jack pine or loblolly pine 
on burns, there will be a variation in age due to natural seeding for 
a period of reproduction which may extend to fifteen or twenty years. 
Stands are termed even-aged if their crowns form practically a single 
canopy or one-storied forest, which is true when the period of repro- 
duction does not exceed approximately one-fifth of the rotation or 
period required to reach full maturity. Where the crown cover of 
stands of mixed ages varies so greatly that it is composed of different 
stories, and must be separated into component age classes whose aver- 
age age is separately distinguished, the stand is termed many-aged 
or in some cases all-aged. The separation of such stand may be either 
directly into age groups, or into groups based on size or diameter with 
a limited range of age, whose average age is sought. 

260. Average Age. Definition and Determination. The average 
age of a group of trees showing a range of ages must be that age which 



338 DETERMINING THE AGE OF STANDS 

indicates or determines the rate of volume production per year at 
which the stand has grown; therefore, the average age must be a 
weighted age based on volume. The determination of average age 
applies only to those stands which fall under the definition of even-aged 
stands, yet have within the hmits of the group a sufficient range of ages 
so as to require a further investigation in order to fix the weighted or 
average age of the group. For many-aged stands, the average age of 
each age class must be determined separately. 

For a given age class or even-aged stand as thus defined, the average 
age is the age which would be required to produce an even-aged stand 
containing the same volume as that of the uneven-aged stand in ques- 
tion. 

The methods possible for determining the weighted average age 
of the trees comprising the age class usually involve the choice of 

1. Treating the entire age class as a single group, or subdividing 

it into from two to three, usually not over two, sub- 
groups. 

2. Determining the average tree, for the entire class, or sepa- 

rately for each sub-group. 

3. Ascertaining the age of these average trees. 

4. Weighting the resultant ages of average trees of sub-groups, 

to determine the weighted average age of the age class. 

261. Determining the Volume and Diameter of Average Trees. 

Subdivision of a group into two or more sub-groups will be made, if at 
all, on the basis of diameters, by the diameter group method (§ 251). 

In determining the average tree for the age class, or for a sub- 
group, there are two reasons for basing this selection on average volume. 
In the first place, if these selected trees are to be felled, and their ages 
taken as indicating that of the stand, the larger trees must be avoided, 
for in aU probability they are advance growth, several years older 
than the rest or possibly belonging to an entirely different age class. 
The smaller trees would also be rejected since they may be late seedlings 
some years younger than the average, or in extreme cases, so badly 
suppressed that a certain number of rings may be lacking and the 
growth difficult to determine. Trees of about average size for the group 
or stand must then be chosen. Where two or more groups are made, 
an average tree for each group is separately selected. 

Volume is the determining factor upon which the weighted average 
age is to be based, hence the tree whose age is taken to indicate that of 
the stand must be a tree whose volume is an average of the stand. 
This principle applies not merely to cubic volume, but to the merchant- 
able volumes expressed in units of product, such as board feet. Since 



DETERMINING AGE OF AVERAGE TREES AND STAND 339 

the purpose of the investigation is to determine the period which will 
produce an equal volume of material in an even-aged stand, the product 
in terms of which this vokuue is measured actually affects the average 
age (§ 260). For board-foot contents which increases more slowly at 
first and more rapidly later in the life of an individual tree, the average 
tree will be larger and older than for cubic contents, since a portion of 
the stand will be rejected altogether and fall in a younger age group 
or else will logically receive a smaller weight in the average for determin- 
ing the equivalent age of an even-aged stand. 

The first step is therefore to determine the volume of the average 
tree of the stand or sub-group. It is evident that the inclusion of a 
large number of trees of the smaller diameters in a large group will 
pull down the volmne of the average tree and tend to unduly lower its 
age. The plan of subdividing age classes into smaller diameter groups 
is chiefly useful in avoiding this tendency to error, and is accomplished 
by throwing together trees varying but little in size, to obtain the 
average. It is of advantage therefore to make two or more of these 
sub-groups where possible. 

When volume is measured in cubic feet, basal area may be sub- 
stituted for volume and the diameter of a tree of average basal area 
determined. To obtain this, the sum of the basal areas of the trees 
in the group is divided by the number of trees to obtain average basal 
area. The diameter of a tree of this area is found in Table LXXVIII, 
Appendix C, p. 490. 

When measured in board feet, the volume of the average tree is 
found directly by dividing the total volume of the stand or of the sub- 
group in board feet by the number of trees. As in case of basal area, 
the diameter of a tree of this volume is now required if sample trees 
are to be felled to determine age. For this purpose a local volume 
table based on diameter is used (§ 142) from which the D.B.H. of 
a tree of the given volume can be determined to within i^-inch. 

262. Determining the Age of Average Trees and of the Stand. The 
age of these selected trees can then be obtained by felling trees of this 
diameter. In stands of variable age from two to three trees are pref- 
erable to one. As a substitute for this method, where it is extremely 
uncertain that the tree selected wiU have the average age, a table of 
diameter growth showing the ages of trees of different diameters may 
be prepared from similar stands in the vicinity. If the average rate 
of growth thus obtained applies to the stand in question, the age of a 
tree of the given diameter may be taken from this curve instead of 
from felled timber. On account of the uncertainty of the correlation 
between the growth figures obtained in this way and of the age of the 
stand in question, the method has not been widely used and the felling 



340 



DETERMINING THE AGE OF STANDS 



of the test trees or their age determination by borings or chopping^ 
is the standard practice in determining the age of stands. When the 
stand is treated as a single group, the average of the ages of the test 
trees, all of which will be of the same average diameter, is taken as the 
age of the stand. When two or more sub-groups have been separated, 
the age of the entire stand must be calculated by weighting the pre- 
determined ages of the sub-groups, in the proper proportions. 

The following illustration will bring out the different methods possible in doing 
this. An " even-aged " stand composed of 30 trees is divided into two groups as 
follows : 



Trees 


Average volume. 
Board feet 


Total volume of group. 
Board feet 


Average age of trees in 
group. 
Years 


10 
20 


500 
125 


5000 
. 2500 


100 
70 



1. If each of these groups occupies an equal area and is given equal weight, the 
average age may be found by adding the ages of the sample trees and dividing by 2. 
This gives eighty-five years, and is known as the arithmetical mean sample tree 
method. This method does not conform to the basic principle of weighted ages 
sought. 

2. When the trees are weighted by number the result is : 

10X100 = 1000 

20 X 70 = 1400 

Total, 2400 -=- 30 = 80 years 

This overemphasizes the number of trees rather than their volume, hence is unsat- 
isfactory. 

3. Trees are weighted by volume on the principle by which weighted volume 
averages are always obtained: 

100 years X 5000 = 500,000 

70 years X2500 = 175,000 

Total, 675,000 -=-7500 = 90 years. This method is acceptable. 

4. The sum of the mean annual growth for the groups is obtained. The total 
volume divided by this sum gives the average age. This method is considered 
by European investigators to be more accurate than the others. As applied: 

5000^100 = 50 

2500 -^- 70 = 35.7 

Total mean annual growth for stand, 85 . 7 

7500^85.7 = 87 years. 

By either method 3 or 4, it is seen that the average age is influenced by volume 
rather than by area or number of trees. 



AGE AS AFFECTED BY SUPPRESSION. ECONOMIC AGE 341 

263. Age as Affected by Suppression. Economic Age. When stands 
are comparatively even-aged and the trees composing them liave grown 
up as dominant individuals, free from suppression, the actual age of 
such trees is a fair indication of the age which an even-aged stand would 
require to produce an equal volume. But under this same definition, 
the age of a tree which has been suppressed in the early period of its 
life does not indicate the required age but one considerably greater. 
The correction of the actual ages of suppressed trees to determine the 
age desired is known as the determination of economic age. What is 
wanted is the rate of growth of an average dominant tree on the same 
site as that occupied by the suppressed trees. Where reproduction 
takes place under a stand either of the same or of a different species, 
the problem of growth is one of having two crops of timber on the same 
land at the same time, and the rate of production per acre is the sum 
of these two successive crops divided by the total period required to 
produce them both. To isolate the period required for a single crop, 
we must determine the rate of growth of the crop as if it were in sole 
possession of the area. 

A composite growth curve may be built up for average trees by 
measuring the growth on these trees only down to the point at which 
they were evidently freed from suppression and substituting from this 
point on the average growth of seedlings and saplings measured on 
dominant specimens. For instance, if the first 2 inches of an average 
tree shows suppression, the average rate up to 2 inches must be taken 
from other dominant, younger trees, and added to the remaining years 
to get the total economic age of the tree in question. This factor has 
been neglected in American growth studies, for the reason that with 
such species but few attempts have been made to determine total 
age, investigators being content with ascertaining growth for short 
period based upon the diameter of the trees. 



CHAPTER XXIV 
GROWTH OF TREES IN DIAMETER 

264. Purposes of Studying Diameter Growth. One purpose of 
studying the growth of trees in diameter is to determine the total volume 
of trees of given ages, or the growth in volume of trees for a short period. 
The volume of trees is based on D.B.H. and height. The diameter 
growth must always be correlated with D.B.H. for the trees measured, 
and height growth is usually required. A second purpose is to determine 
the dimensions or sizes reached by trees in a given period. 

265. The Basis for Determining Diameter Growth for Trees. It 
is impractical to cut sections at B.H. for growth measurements. Not 
only is there a needless waste of timber, but the labor of felling and sec- 
tioning the tree may also be avoided if the measurements are taken 
at the stump following logging operations. Where current growth for 
short periods is tested with an increment borer (§ 277) the measure- 
ment is taken at D.B.H. The growth measurements on stumps require 
three steps to determine the ages of trees of given D.B.H. outside the 
bark; namely, 

1. Diameter growth on the stvunp. 

2. Correction for age of the seedling. 

3. Correlation between stump diameter inside bark and D.B.H. 

outside bark. 
As diameter increases rapidly at the stump, the lower a stump is 
cut the greater will be the apparent rate of growth for the tree. Stump 
height classes differing by 6 inches may be made in growth studies, 
but this is not often done. Stump heights usually vary with stump 
diameters in a ratio of from one-third to two-thirds of the diameter, 
depending on the closeness of utilization. For a given region and 
standard, the stump heights for given diameters are fairly constant 
and the average rate of growth is found for stumps of each diameter 
with all stumji heights averaged together. 

266. The Measurement of Diameter Growth on Sections. The 
section measured must be at right angles with the axis of the bole. 
In stumps this means a horizontal cross cut. Slanting cross cuts exag- 
gerate the length of the radius and result in a slight plus error in growth 
measurements. The procedure is as follows: 

312 



MEASUREMENT OF DIAMETER GROWTH ON SECTIONS 343 




Fig. 67. — Stump sec- 
tion fifty years old 
showing eccentric 
growth, position of 
the two average 
radii AB and AC 
and rot (jn radius 
AB. Decades of 
growth are shown. 
The growth must be 
measured on radius 
AC. 



An average radius is located. Its length must equal just one-half 
of the average diameter inside bark (§ 25). To determine the average 
diameter, calipers graduated to yV-inch may be used (§ 189). In all 
cross sections which are not perfect circles, the 
lengths of the radii from the pith or center of 
growth vary more widely than the diameters owing 
to the fact that the pith is always located at one 
side of the geometric center of the cross section. 
Leaning trees grow largely on the under side and 
this general law accounts for the position of the 
pith. On an eccentric cross section there are but 
two radii which are average in length and can be 
measured for growth. It often happens that one 
or both of these radii (Fig. 67) are interfered with 
either by the undercut or by the presence of rot 
or deiacts which prevent growth measurement. 
If either one is clear, the section may be meas- 
ured. Otherwise, if measurement is absolutely 
necessary, a longer or shorter radius can be taken 
and the measurements reduced by proportion to 
the required length.^ 

Method of Counting Decades. The next step is to count the number 
of annual rings and indicate with a pencil the points at which the decades 
fall. Except in scientific investigations where each year's growth may 
be separately measured to determine the influence of climate on annual 
growth, the decade is ordinarily the smallest interval used in measure- 
ment of diameter growth. For current periodic growth a five-year 
period is sometimes used in order to get points for a curve in predicting 
the growth (§ 279). 

Unless the total age of the stump falls on a decade, as thirty, or 
forty years, there will be one fractional decade laid off, representing 
from one to nine years, depending on this total age. The diameter 
growth is always measured outivard beginning with the pith or center 
of growth. But in counting the annual rings to lay off these decades 
of growth, two distinct methods of procedure are followed. In one, 
the count begins at the center, laying off ten years from the pith, and 
throwing the fractional decade to the outside as on the right side of 
Fig. 68. By the other, the count begins at the cambium layer or 
outer ring, and this throws the fractional decade to the center as on 
the left side of the figure. 

Purpose of Counting Inward from Outer Ring to Center. The choice 

^ E.g., if the average radius is 9 inches, and a radius of 10 inches is measured, 
each measurement must be reduced by the factor ^ or .9 



344 



GROWTH OF TREES IN DIAMETER 



of these methods is based on the purpose of the study. In all measure- 
ments of diameter growth, an average rate is to be found by combining 
the growth of a large number of trees. This means averaging together 
the growth by decades. The trees so averaged usually differ in age, 
sometimes over a v/ide range. The growth of the last decade, or current 
periodic growth on all trees, regardless of their total age, is represented 
by the outside or last ten rings. Any influence, such as cutting, fire or 
climate, which affects diameter growth, must be studied on the basis 
of current growth. In making a tree analysis, which requires the growth 



Inner Bark 
Outer Bark 




Fig. 68. — Alternate methods of counting and measuring annual rings on a cross 
section 36 years old. On left, rings are counted in decades beginning with 
outer ring. On right, count begins with center and odd rings fall on outside. 

in diameter of upper sections (§ 289) the separation of the growth in 
volume for each past decade requires the measurement of the same 
ten rings on each of the sections analyzed. This is secured by counting 
back from the outer ring. When growth is studied for these purposes, 
rings must always be counted from the outside inward. In this case 
the first measurement from the pith outward will be the fractional 
decade. The average growth for this period represents the average 
number of years less than 10 which were measured. This may vary 
from 1 to 9 years but tends to average 5 years. The second decade 
wall include, on different trees, the years 2 to 19, the third, 12 to 29; 



MEASUREMENT OF DIAMETER GROWTH ON SECTIONS 345 





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346 GROWTH OF TREES IN DIAMETER 

e.g., on a tree 21 years old, the decades are 1, 2-11, 12-21 years. On 
a tree 29 years old the decades are 9, 10-19, 20-29 years. 

Purpose of Counting Outward from Center to Outer Ring. In tracing the growth 
of trees in diameter, based on their age, to determine tlie average sizes reached at 
each decade, the above averages might tend to conceal or flatten out any changes 
characteristic of the juvenile period. In this case a more clear-cut definition of 
growth may be obtained if age is actually made the basis, and the same decades 
averaged for each stump, e.g., 1-10, 11-20 years. 

For this purpose the count would be made outward from the pith, coinciding in 
direction with the measurement of growth, throwing the fraction to the outside. 
But this causes the fractional decades to fall in as many different columns as there 
are trees of different ages by decades. In tree analyses it would result in measur- 
ing different fractions at each upper section instead of the same rings. It does 
not give current diameter growth for a stand. The age of the seedling, which is 
usually a fractional decade, must still be added. For these reasons the first method 
is considered standard. But for the purpose indicated, diameter growth based on 
age, the last fractional decade on the outside although recorded could be dropped 
in obtaining average gi'owth of several trees; e.g., a 43-year stump can be computed 
for its first four decades only. By this plan, the averaging is simi^lified. 

Method of Measurement. The measurement of diameter growth is 
usually made with a steel rule graduated to inches and twentieths, or 
.05 inch, which is the smallest graduation commonly employed. 
When the radius has been laid off and each decade marked, the zero 
of the rule is placed at the center and the distance read to each decade 
point. The measurements are cumulative, that is, the rule remains 
in the same position until the complete radius is read. This avoids 
errors which are sure to occur in moving the zero from one decade 
to another to separate the decade measurements. The form of record 
is shown on p. 345. The accuracy of the reading should be checked 
by noting that twice the total radius should equal the average diameter. 

267. The Determination of Average Diameter Growth from the 
Original Data. The average diameter growth for the trees measured 
may be obtained by arithmetical means, and by the aid of graphic 
methods. 

Table LI shows the method of computing the average growth. 
When the decades have been counted from the pith with the final 
fraction rejected, each decade is full and the averages fall at 10, 20, 
30 years, etc. This completes the table in the form desired. But 
when the rings are counted from the outside, the first decade being 
fractional, the growth is not shown for full decades, but for odd years 
as 7, 17, 27 years, etc. 

To obtain the growth at the required decades, a curve of radius 
growth based on age is plotted as shown in Fig. 69, each point being 
plotted above its proper age. The radius scale is then doubled to 



AVERAGE DIAMETER GROWTH FROM ORIGINAL DATA 347 



read directly in diameter growth. From this curve, the growth at 
10, 20, 30 years, etc., is then read for the table. 





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Radius, Inches 

(Double to read Diameter) 

Fig. 69. — Growth in radius of 5 spruce trees plotted separately, and curve of average 
growth. The average number of years in first fractional decade is 7. The 
successive decade averages are plotted on 17, 27, etc. The last three points 
represent averages based on less than five trees and should not be plotted on 
the same curve. 

The growth of each tree is shown by curves. In plotting data for a 
growth curve the points plotted for single trees would not ordinarily be con- 
nected. The average would either be sketched by eye, or plotted from the 
position of the average points as indicated. 

Substitution of Graphic for Arithmetical Method. For this computation 
graphic plotting of the original data is sometimes substituted. This method is also 



348 GROWTH OF TREES IN DIAMETER 

illustrated in Fig. 69, in which the growth of five spruce trees is plotted, their rings 
being counted from the outside inward. Each tree is plotted on the exact years on 
which its measurements fall as determined by its total age. Where a large number 
of trees are plotted, the points .are not connected but form a band, on which the 
curve of average growth is sketched by eye. This method is intended to save the 
labor of calculating the averages arithmetically. 

Where trees of different ages are included in the average, the upper extremity of 
the growth curve will represent a smaller number of trees, whose growth, if dominant, 
will exceed the average rate, but if suppressed, will fah below it, causing the curve 
to depart from a true growth curve, as illustrated in this Figure. 

268. Correction of Basis of Diameter Growth on Stump to Conform 
to Total Age of Tree. The next step is to correlate this curve of growth 
with the total age of the tree. The average age of seedlings must be 
determined for the given average stump height (§257). The number 
of years thus indicated is added to the scale by moving the zero the 
required number of points to the left. This new zero causes a shift 
in the age of each section to correspond. The curve now shows, not 
the diameter of stump sedicns of various ages, but the diameter of 
trees of various ages when measured at the height of the stump. 

269. Correlation of Stump Growth with D.B.H. of Tree, The third 
step is to determine the D.B.H. for these same trees in order to correlate 
this with age. What is desired is not the age of the section at B.H. 
but the D.B.H. of the tree, whose total age and growth at stump are now 
known. 

A tree of a given stump diameter, whose total age has been found, 
has a set of upper diameters or tapers representing its form, as expressed 
in a taper table (§ 167). Of these the most important is D.B.H. This 
third step then consists simply of determining the average taper of the 
butt, from stump height to B.H. so as to find the D.B.H. corresponding 
to each inch stump-diameter class. 

Standard stump tapers show the D.I.B. (§135) of stumps at heights 
of 1, 2, 3, 4, and 4§ feet, corresponding to each D.B.H. class. But 
to determine growth of trees at B.H. corresponding to growth on the 
stump inside the bark, heights of stumps are usually averaged, and a 
direct comparison is made of average D.B.H. outside bark with average 
D.I.B. on the stump for all trees falling in the given stump-diameter 
class. 

Stump tapers may be taken on the butt logs of felled trees in the 
measurement of volumes (§ 168). The number of measurements so 
obtained is often insufficient and may be supplemented by measuring 
the diameter at stump height and width of bark to get D.I.B., on stand- 
ing trees, together with D.B.H. Owing to the great variation in diam- 
eters at the stump compared with D.B.H., a large number of stump 
tapers are required to produce a curve free from irregularities, as illus- 



CORRELATION OF STUMP GROWTH WITH D.B.H. OF TREE 349 

trated in Fig. 70 for loblolly pine. These data can be obtained verj^ 
rapidly and without much extra cost. 

These stump tapers are then classified on the basis of stun.p diam- 
eter inside bark and not on D.B.H. since they are to be plotted on the 
curve of stump diameter. An arithmetical average of these relations 
is obtained, and expressed in the form of Table LII (p. 3£0). 




8 10 



20 30 40 

Age of Tree including Seedling 



50 



Fig. 70. — Diameters, inside bark at stump, outside bark at B.H., and inside bark 
at 16 feet above stump, for trees at different ages. Loblolly pine, old fields, 
Urania, La. 



The D.B.H. outside bark for each stump-diameter class is now 
plotted on the curve of D.I.B. on the stump as shown in Fig. 70. Since 
this curve is based on age of tree, the diameter at any point on the 
bole of a tree of a given age will fall on the indicated vertical line cor- 
responding to this age. Thus, a tree measuring 14 inches on the stump 
in Table LH is 30 years old at the stump, and 33 years old when 
corrected for age of seedling which is 8 years. The D.B.H. for a 14- 
inch stump is 13.2 inches, which is plotted above 33 years. In the 
same way, D.I.B. at the top of the first 16-foot log, which is 10.8 inches, 
would fall above the same 33-year point on the scale. In this manner 
the stump tapers are each plotted by first finding the corresponding 



550 



GROWTH OF TREES IN DIAMETER 



D.I.B. at stump, on the curve of growth, which indicates the required 
age of the tree above which the remaining dimensions are to be plotted. 

TABLE LII 

Stump Tapers — Based on Stump DIB. for Stumps 1 Foot High 

Loblolly Pine, Urania, La. 



Stump diameter 
class. 


Average D.I.B. 
stump. 


Average D.B.H. 


Inches 


Inches 


Inches 


5 


5 1 


4.5 


6 


6.0 


6.1 


7 


6.8 


6.8 


8 


8.2 


7.0 


9 


9.1 


8.3 


10 


10.0 


9.6 


11 


11.1 


10.4 


12 


11.9 


11.0 


13 


13.2 


12.3 


14 


14.1 


12.7 


15 


15.1 


12.9 


16 


16.0 


15.6 


17 


17.2 


15.8 


18 


17.8 


16.7 


19 


• 18.7 


18.2 



The D.B.H. 's for different stump diameters are now connected by 
a curve, which shows D.B.H. for trees of intervening ages, and for 
all stump diameters. From this curve the D.B.H. corresponding to 
each decade in the li e of the tree can be read, in the form of Table 
LHI. 

TABLE LIII 
Growth of Loblolly Pine, Old Field, in D.B.H., Based on Age of Tree, 

Urania, La. 







Diameter at top 


Age. 


D.B.H. 


of first 16-foot 
log inside bark. 


Years 


Inches 


Inches 


10 


3.6 


1.0 


20 


9.8 


7.0 


30 


12.5 


9.9 


40 


14.7 


12.0 


50 


17.0 


13.8 



DIAMETER GROWTH OF TREES GROWING IN STANDS 351 

Since there can be no D.I.B. at 16 feet until the tree has reached 
this point in height, the curve of these points would terminate at zero 
diameter at an age equal to that required for the tree to grow 16 feet 
in height, above the stump, which is 8 years in Fig. 70. In the same 
manner the D.B.H. curve would terminate at a point representing the 
year in which the tree reached 4| feet in height, which is 4 years. The 
stump curve has already been shown to terminate at an age repre- 
senting the growth of the seedling to stump height at 3 years. This 
principle is later explained more fully in connection with a method 
of plotting the volume growth of different trees (§ 291). 

270. Factors Influencing the Diameter Growth of Trees Growing 
in Stands. Diameter is the most variable factor of tree growth, dif- 
fering with a wider range of conditions and showing greater diversity 
between trees in the same stand than height growth. Growth in diam- 
eter influences growth in volume of the tree to a much greater extent 
than does height growth, the relation being that of (P or area. Since 

irdr 
the growth in area bears this fixed relation ——, the area growth of indi- 
vidual trees is never studied, as all problems for which it is desired 
are solved by the study of diameter growth. The rate of diameter 
growth is determined by four factors: species, quality of site, density 
of stand, and crown class. 

Secondary factors modifying diameter growth are the amount of 
shade endured by the specific trees studied, and the treatment of 
the stand. 

271. Effect of Species on Diameter Growth. Different species 
have developed specific differences in average rate of diameter growth. 
Those accustomed to growing on soil of good quality as dominant 
species have acquired the fastest growth rate. Intolerant trees usually 
grow faster than tolerant since they must maintain their dominance. 
Of this, the cottonwood is an example. Trees which have the power 
of enduring shade usually grow, even in the open, at a somewhat slower 
rate than intolerant trees. 

Trees do not indefinitely maintain a given rate of diameter groT/th. 
Until a tree actually dies, it continues to increase in diameter, but there 
comes a period when, in spite of the dominant position of the tree, 
its rate of diameter growth diminishes. The period at which this 
diminution sets in marks the maturity and the beginning of decadence 
of the tree. The life cycle of different species of trees is as distinct 
as that of different animals. Short-lived trees, like jack pine and 
tamarack, show this falling off at 70 or 80 years or sooner, and disappear 
within 30 or 40 years thereafter. The same is true of aspen. The life 
cycle of conifers is apparently affected by general climatic conditions. 



352 GROWTH OF TREES IN DIAMETER 

That of western conifers is double the cycle characteristic of those 
in the East, while that for redwoods and Sequoia is fully five times 
as great as for most of the remaining western conifers. 

The life cycle of any individual tree is governed by the average for 
the species but appears to depend on size and not age. A tree is mature 
when it has reached the maximum size permitted by its site and vigor 
of crown, whether this is secured by continuous rapid growth as a 
dominant tree or is delayed by a period of suppression. Trees character- 
istically intolerant and dominant, and accidentally suppressed in youth, 
if they recover from this suppression, will add the period of suppression 
to the average age which they attain and contmuc to grow until they 
reach the usual size. Trees naturally undergoing and recovering from 
a period of suppression, such as spruce and balsam, may attain maturity 
under these conditions 100 years later than trees of the same species 
growing in the open, and their life cycle will be that much longer. This 
law was also found to hold true for the Sequoia gigantea.^ 

272. Effect of Quality of Site. The greater productive capacity 
of better sites is reflected in the increased rate of growth in diameter 
of the species on these sites. Either deficiency or continuous excess 
of moisture greatly reduces the site quality and slows down diameter 
growth. The final expression of site quality is found in terms of total 
volume or rate of growth per year, of which this average diameter 
growth is one of the best indications. 

273. Effect of Density of Stand. The rate of growth of the individ- 
ual or average tree is profoundly influenced by the number of trees 
in the stand. The original number of trees germinating and becoming 
established on a site bears no relation to the number which may grow 
to maturity. The reduction of numbers with increased size and crown 
spread is accomplished by competition between individuals, resulting 
in the death of the weaker trees. With species which become estab- 
lished in dense stands in a single year and maintain an even height 
growth, the inability of the stand to differentiate itself and destroy 
the necessary proportion of the weaker trees is reflected in a great 
reduction in diameter growth on all of the trees. Of this tendency, 
lodgepole pine gives the best examples. In almost all species of conifers 
and many hardwoods, dense, even stocking, unless artificially corrected 
by thinning, gives a much lower rate of diameter growth than the aver- 
age which may and should be secured by the species. Diameter growth 
is therefore apt to be greatly reduced by increased number of trees 
per acre in the stand, or overstocking. 

" Ellsworth Huntingdon, The Climatic Factor, as Illustrated in Arid America, 
Carnegie Institution of Wash., D. C, 1914, Chap. XII. 



EFFECT OF CROWN CLASS 35a 

274, Effect of Crown Class. The individual rate of diameter 
growth varies over a wide range with the same species, site and stand. 
The rate of growth is coordinated dii'ectly with the ci'own spread of 
the tree. There exists a relation between width of crown and diameter 
which is found to hold good under almost every condition and for every 
species, although varying with the species and its habit of growth. 
This law, which might be of great use in determining the number of 
trees which should exist per acre for a given species in mixed stands, 
is somewhat interfered with by the fact that the volume of the crown, 
rather than its mere diameter, is the factor affecting diameter growth, 
and with western conifers, with very tall and slender crowns, width 
alone does not properly express this value. As crowns receive more 
growing space and expand, diameter growth correspondingly increases. 
This elasticity of diameter growth correlated with crown spread is the 
principal means of adjustment which a stand of trees possesses, by 
which it constantly tends to fill in blanks and form a complete crown 
canopy provided only that the distribution of the trees is such as to bring 
these blanks within the possible maximum spread of individual crowns. 

Effect of Shade. Diameter growth during the life of a tree de- 
pends upon its history with respect to the remaining trees in the stand. 
A tree which has remained dominant since germination maintains a 
maximum rate of diameter growth. The crown spread at successive 
decades is a maximum. Trees which are at first dominant and later 
suppressed, cease to grow in diameter because their crowns cease to 
expand. The relation between diameter and crown is maintained, 
but neither continues to increase. Trees which were originally sup- 
pressed and later freed may show a marked increase in diameter growth 
coinciding with an increased spread of crown, thus maintaining the 
proportion under the changed conditions. But if their crowns have 
lost the power to recuperate, which depends upon both the specific 
character and the age of the tree, no increase is made in diameter 
growth by reason of this liberation. 

Effect of Treatment. The growth in diameter of trees can be pro- 
foundly influenced by the artificial treatment of a stand. Since for 
the individual tree it is a function of crown spread and its rate is governed 
by the ability of the crown to expand, diameter growth is the most 
easily governed and most adaptable function of tree growth. The 
stand per acre or rate of growth for a period measured in cubic contents 
may not be subject to great modification, but the sizes of the stock 
produced and consequently the value per acre can be greatly influ- 
enced by management. The behavior of trees in thinned stands and 
on cutover lands must be studied separately from those subjected to 
the natural laws of survival in original unthinned forests. 



354 GROWTH OF TREES IN DIAMETER 

275. Laws of Diameter Growth in Even-aged Stands, Based on 
Age. The struggle of the individual trees for space produces different 
results in even-aged and in many-aged stands, although the general 
effect is a final reduction in numbers in either case. In the even-aged 
stand the area occupied by an age class is definitely fixed. Expansion 
of the crowns of individual trees can occur only by the prevention of 
corresponding expansion of other crowns and by securing of additional 
space through the actual death of the weaker trees. This process 
results in a continuous differentiation of diameter classes in an even- 
aged stand with advancing age. As the trees become fewer in number, 
the difference in size of the survivors increases. These relations are 
shown in Fig. 71, in which the number of diameter classes existing at 
different ages in an even-aged stand is indicated. 

The growth in diameter of the trees which compose this even-aged 
stand is shown in Fig. 72. The diminution in diameter growth due 
to suppression of crowns affects successive trees of larger and larger 
diameter. The average tree at a given decade is seen to fall into the 
lower half of the stand in the succeeding decade and at some future 
period will become suppressed and finally die. 

In Fig. 71 is shown the difference in basis and composition of the curves based 
respectively on age and on diameter. The curve based on age in this figure is 
composed of averages of all the diameter classes in successive even-aged stands, as 
shown in the vertical columns. The curve based on diameter takes all trees of a 
given diameter for each successive average, thus including trees from a number 
of different age classes or stands as read horizontally in the diagram. This curve as 
plotted in Fig. 71 is reversed, with the basis, diameter, plotted on the vertical scale. 
The proper form of such a curve is shown in Fig. 73. The wide divergence possible 
in the two bases, for dominant larger trees, is indicated in Fig. 71. 

It is evident that growth measurements of diameter based on age, which include 
trees whose total age varies from 20 to 50 years, corresponding with the diameter 
classes A to L in Fig. 72, will not be correct for any single tree in the stand D. The 
portion of this curve representing the earlier decades is depressed or lowered by the 
inclusion of the slower growing trees F to L which afterwards die. With the suc- 
cessive dropping out of these trees from the average, the latter portion of the 
curve shows a more I'apid growth than that of the trees which compose it. 

To get the actual past growth of an average tree for a stand of a given age, C, it 
is evident that only trees which have reached this age must be measured, A to E. 
To secure average diameter growth for mature timber which in the future will be 
gi-own to the given sizes and numbers per acre characteristic of this class of timber, it 
is incorrect to include measurements of average trees for stands which have not yet 
reached this age, F to L. By confining the selection of trees to timber of the desired 
age and by taking the growth of all of the trees found on an area of sufficient size, 
we obtain an average rate, showing the past growth of these trees, which is a true 
growth curve, C. If it is desired to predict the rate of growth for the average tree of 
a given age and character of mature stand, dominant trees must be selected from 
younger stands rather than the average tree. The fewer of these trees, and the 
greater their relative crown spread or dominance compared to the remaining stand. 



LAWS OF DIAMETER GROWTH IN EVEN-AGED STANDS 355 

the greater the age with which the resulting growth curve will coincide as an expres- 
sion of yield per acre and average tree; e.g., for predicting the growth to 35 years of 
stands now 20 years old, the group of trees, A to H, whose average tree is D, must be 
included, omitting classes J to L which would lower the average tree at 20 years 
to F. 




35 45 

Age, Y"ears 

Fig. 71. — Number of trees in each diameter class in normal stands at four successive 
ages, and resulting curves, when averaged respectively on basis of age and of 
diameter. 



The composite curve of average growth in which each successive decade is based 
on a lesser number of trees than the preceding period, is a useful tabulation to show 
the average diameter of surviving trees at given ages, but as shown does not correctly 
indicate the progress of growth for any of the trees on which it is based, unless it is 
confined to a given number of trees throughout. 



356 



GROWTH OF TREES IN DIAMETER 



Diameter growth based upon age is used, in practical studies, princi- 
pally as an aid in indicating the difference in rate of growth of species, 
sites, and different methods of treatment and as an aid in determining 
the average age of stands in the forest under different conditions. 
This application is much more limited than is commonly supposed 



26 
24 
22 

20 
18 

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Age, Years 

Fig. 72. — Differentiation of diameter growth as result of different rates of develop- 
ment of crowns, in normal stands, even-aged. 



since for many problems the substitution of yields per acre based directly 
on total age answers the questions more directly and accurately, while 
for forests in which the average age for stands cannot be ascertained, 
diameter growth is not based on total age, but on diameter classes 
(§ 336). 



LAWS OF DIAMETER GROWTH IN MANY-AG'ED STANDS 357 



276. Laws of Diameter Growth in Many-aged Stands, Based on 
Diameter. Wlien diameter growth is studied in order to determine 
the age of trees of given diameters, the basis of the average is entirely 
different from that required when the diameter or size of trees of given 
ages is required. By the inspection of Fig. 71, it will be seen that 
when based on age for each decade, several different diameter classes 
are averaged together. The average diameter even for the oldest 
age class is several inches less than the maximum diameters reached 
by the dominant trees. To prolong a curve of growth based on age 
until the diameter of the maximum tree is reached, would add several 
decades to the apparent age of a tree of this diameter. 

On the other hand, if diameter is actually the basis and the average 
age is sought, the classes included to obtain these averages are read 
horizontally in Fig. 71 and include under the same diameter several 
different age classes. The principal effect of this difference in the basis 
of averaging is found when the larger diameters are reached. In 
stands composed wholly of intolerant trees, where suppression and 
prolonging of the life cycle is not a factor, the difference between the 
age of the larger, dominant diameter classes which exceed the average 
and the average age of smaller diameter classes, which include many 
trees fully as old as the dominant classes, is much less than would be 
indicated by a curve based on age. A curve showing the average age 
of trees of given diameter is not expected to show the progress of trees 
in diameter from dec- 
ade to decade, but 
expresses directly the 
result of the total 
growth or period for the 
specific class of trees 
concerned. 

There is but one 
way to determine ac- 
curately the average 
age of trees of separate 
diameter classes and 
that is by a total count 
of rings for several trees Fig. 73.— Ages of trees of different diameters, shown 
in each diameter class for two groups of longleaf pine, the first com- 
to obtain the average posed of second-growth stands, the second of 
age dnectly on this veteran or old-growth timber, 
diameter basis. When 

these points or averages are plotted, they will show a relation about 
as indicated in Fig. 73. 







































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-- 


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k-- 








190 


























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358 GROWTH OF TREES IN DIAMETER 

The application of such a growth study is to determine correctly 
the average age of trees of given diameter classes and diameter groups 
in a forest or stand when the basis of age for the stand cannot be directly 
determined (§320). This presupposes that the stands are not even- 
aged, but many-aged in character. In mixed many-aged stands or 
groups, suppression usually plays a large role and again interferes with 
this determination by requiring the substitution of the economic age 
for the actual age (§263). But for the species such as the Southern 
pines, which are fireproof to a certain extent, and the Western yellow 
pine, for the same reason, the age groups may be intermingled and yet 
the dominant character of growth maintained. Under these circum- 
stances, the direct determination of age based on diameter may be 
used for determining the average age of diameter groups, especially 
for the upper or dominant classes. 

277. Current Periodic Growth Based on Diameter Classes. The 
Increment Borer. A more common application of growth based on 
diameter classes is for the prediction of current periodic growth in specific 
stands, for short periods, by predicting the growth of each tree in the 
stand in diameter and correlating this data with volume growth. The 
drawbacks to this method have been discussed in § 251. Dealing, 
as it does, with the specific stand and actual number of trees, it 
is directly applicable to stands of all degrees of density and to 
the actual stocking found on the ground, and to this extent is 
applicable directly to the existing forest without the necessity 
for a yield table. Tables showing the growth in diameter which 
may be expected of trees of given diameters may be applied directly 
to stand tables showing the number of trees of these diameters on 
the average acre. 

The current growth of trees of given diameter is measured either 
on the stump or directly at B.H. Growth measurements taken on the 
stump must be laid out on an average radius (§ 25). As the growth 
in D.B.H. outside bark is frequently less than that on the stump inside 
bark (§ 269) correct results would require the reduction of the radial 
growth on the stump to its equivalent at D.B.H. This is not usually 
done, first because for trees of the smaller diameters D.O.B. at B.H. 
tends to coincide with D.I.B. on the stump; second, because the total 
error thus incurred in measuring the growth based on age is proportion- 
ately reduced in measuring current growth, although the percentage 
of error remains the same. This may be considered too small to require 
correction. When measured directly at B.H., it is important to secure 
an average radius if possible. The only method by which this can be 
done is to take two readings on opposite sides of the tree, and determine 
the mean. 



CURRENT PERIODIC GROWTH BASED ON DIAMETER CLASSES 359 



The increment borer (Fig. 74) can be used for measuring radial 
growth at B.H. This instrument consists of three parts: 

(a) A hollow auger, A, from 4 to 10 inches long, tapering and 
threaded at one end, and square in cross section at the other end. 

(b) A hollow metal handle, B, with a square opening in the center 
into which the auger fits when in use. At the ends of this handle are 
detachable caps. 

(c) A narrow wedge, C, furnished at one end with a flat head, and 
incised on one side at the other end. 






Fig. 74. — Increment borer, showing construction. 

The wedge and the auger are carried inside the hollow handle when 
the instrument is not in use. 

To use the instrument one bores into a tree to the desired depth, 
then inserts the wedge through the auger with the incised ^'de turned 
inward. The wedge is jammed down, thus holding tightly in place 
the core of wood within the auger. The handle is then turned sharply 
to the left, severing the core from the wood. The cylinder of wood is 
then drawn out, and the rings counted or measured. 

The best type of instrument is made in Sweden, and cores of from 
6 to 8 inches may be secured by the larger sizes. The instrument is 
easily taken apart and is convenient to carry. When taken at B.H. 



360 



GROWTH OF TREE8 IN DIAMETER 



these measurements require no correction. Care must be taken if 
but a single measurement is made on standing trees, to select the point 
for testing on neithec the lower nor the upper side of a leaniug tree, 
the growth of which is very eccentric, coinciding with its position. 

278. Method Based on Comparison of Growth for Diameter Classes. 
In Chapter XXII it was shown that growth is measured in order that 
future growth may be predicted. This may be done either by pro- 
jecting the growth of a past period into the future on the specific trees 
or stands measured, or by the method of comparing the growth on 
trees or stands which have reached a certain size or age, with younger 
or smaller trees which are assumed to grow at a like rate. These 
principles must be applied in utilizing the growth of trees for determin- 
ing that of stands. 

Since diameter, not age, is now the basis of the growth study, trees 
are classified for growth on the basis of their present diameters at 
B.H. and an average rate is determined for each class. The result of 
such a study is applied to trees of given diameter classes in the stand 
or forest. By the method of comparison, a tree now 15 inches in 
diameter which has grown 1 inch in the last 8 years, was 14 inches 
D.B.H. 8 years ago, and trees now 14 inches D.B.H. if compared with 
this growth, will presumably grow at like rate for 8 years. 

This requires current growth to be measured by inches of diameter, 
or half-inches of radius, and not by decades or periods, in order that 
the basis of c.omparison, D.B.H. classes in the past, may be obtained. 
The rings in successive half-inches of radius are counted and averaged, 
by diameter classes, in the folloAving form: 



TABLE LIV 

Current Growth of Spruce, Adirondacks Region, New York 



Present 


Number of rings 


Diameter to 


diameter. 


in last inch of 


which applied. 


Inches 


diameter 


Inches 


5 


6.5 


4 


6 


5.0 


5 


7 


5.3 


6 


8 


6.6 


7 


9 


5.4 


8 


10 


5.1 


9 



PROJECTION OF GROWTH BY DIAMETER CLASSES 361 

By plotting the values in column 2 on the basis of diameter, a curve 
may be drawn to even out the irregularities shown. To apply such 
a table in predicting growth for a period of 20 years, for 4-inch trees, 
the growth of successive inch classes is used; e.g., the 4-inch tree takes 
6.5 years to reach 5 inches, 5 years to reach 6 inches, and 5.3 years to 
reach 7 inches, or a total of 16.8 years. The next inch requires 6.6 
years, 3.2 of which lie in the 20-year period, equivalent to about |-inch. 
The tree will grow to be 71 inches in diameter in 20 years. In this 
way the growth for each D.B.H. class can be predicted for any given 
period on the assumption that the l)asis of comparison is trustworthy. 
This is the simplest method of growth prediction for trees in many- 
aged forests. In obtaining the average number of years in the last 
inch, all trees included in the table must be measured for the same 
period, i.e., the basis must be ^-inch of radius. If instead the last 
20 years is measured, divided into half -inches of radius, and a fast- 
growing tree used in the table as the equivalent of several smaller inch 
classes, its influence on the average will be increased in like proportion 
and too rapid an average rate obtained. 

Where trees are measured for a past decade or fixed period of years, 
the results are expressed as growth in inches for the period. This rate 
of growth may then be reduced to mean periodic growth (average 
growth per year for the period). Dividing 1 inch by this annual 
growth gives the number of years required to grow an inch 
in diameter for each inch class. This method is equally reliable, and 
most tables of current diameter growth have been derived in this 
manner. 

The assumption underlying the basis of comparison, namely, that 
the rate of diameter growth is a function of diameter, is most nearly 
approximated in many-aged forests of tolerant species such as spruce 
and for averages which include a wide range of ages and condi- 
tions. 

279. Method Based on Projection of Growth by Diameter Classes. 
For single stands or specific conditions, growth for trees of the same 
diameter varies tremendously (§ 274 and § 275) and shows its greatest 
diversity, first in even-aged stands, second, between open-grown and 
shaded trees. For such problems, prediction based on past growth 
of the present trees, rather than comparison, is a more reliable 
method. 

For this purpose, past current growth is measured for the last 5- or 
10-year period, or for two to four such periods, as required. If it is 
assumed that future diameter growth will equal past growth, the growth 
is tabulated as follows: 



362 



GROWTH OF TREES IN DIAMETER 



TABLE LV 
Short-leaf Pine, Louisiana 
Growth by Diameter Classes 



D.B.H. 


Growth in 
10 Years. 


D.B.H. 


Growth in 
10 Years. 


Inches 


Inches 


Inches 


Inches 


10 


1.03 


16 


1.76 


11 


1.60 


17 


1.82 


12 


1.36 


18 


1.84 


13 


1.44 


19 


1.78 


14 


1.67 


20 


2.05 


15 


1.52 








Fig. 75. — Method of predicting 
future growth of trees of differ- 
ent diameter classes based on past 
growth in diameter and harmon- 
ized curves. Loblolly pine, La. 



These values can be evened off 
as described for Table LIV (p. 360). 

This assumption of unchanging 
future diameter growth is a make- 
shift, inaccurate under most con- 
ditions and not as reliable as the 
method of comparison. But by 
measuring the growth for two or 
three periods, which for the pur- 
pose are preferably shortened to 
5 years so as to bring out any 
recent tendencies of current growth, 
the past growth of trees of each 
diameter class may be used to pre- 
dict future growth by means of a 
curve drawn through these past 
points (Fig. 75). 

The original data, and the re- 
sultant prediction of growth are 
shown in Table LVL 

The advantages of this method 
show most distinctly with even- 
aged stands, in which case the 
flattening out or termination of 
the curve of the lowest diameter 
classes occurs successively, and in- 
dicates the death of these smaller 
trees by suppression. 



INCREASED GROWTH. METHOD OF DETERMINATION 363 



TABLE LVI 
Current Growth, Loblolly Pine, by Diameters 





Growth 


IN Past 


Growth in Future 


D.B.H. 












10 Years. 


20 Years. 


10 Years. 


20 Years. 


Inches 


Inches 


Inches 


Inches 


Inches 


10 


0.76 


2.26 


0.3 




11 


.76 


2.24 


.3 




12 


.77 


2,19 


.4 


0.6 


13 


1.00 


2.50 


.5 


.8 


14 


.82 


2.40 


.6 


1.0 


15 


.80 


2.90 


.7 


1.0 


16 


.76 


1.77 


.7 


11 


17 


1 22 


3.32 


.7 


1.2 


18 


.75 


2.23 


.7 


1.2 


19 


1.33 


2.77 


.6 


1.1 


20 


.77 


1.83 


.6 


1.0 



280. Increased Growth. Method of Determination. The effect on 
diameter growth of trees of releasing their crowns by removal of a portion 
of the stand in logging cannot be predicted accurately on stands pre- 
vious to cutting. The release of additional supplies of soU moisture 
and fertility, increased light and other favorable influences, is not deter- 
minative. The ability of the tree to take advantage of these favorable 
circumstances varies with the age and vigor of the individual crown. 
When trees have passed a certain relative age and have become over- 
mature, they no longer respond as vigorously, and some species make 
no response at all, while others, such as lodgepole pine, seem to retain 
the power of increasing their growth throughout their life. Some trees 
are not released in partial cuttings; hence increased growth cannot 
be expected except on those trees which are benefited and have the 
power of response. 

The factor of increased growth after cutting must therefore be meas- 
ured by studying trees growing on tracts which have been cut over at 
some previous period coinciding in length with the period for which 
the prediction of growth is desired. This may be 10, 20 or 30 years. 
Increase in growth due to cutting tends to disappear as the stand 
adjusts itself to the new conditions and closes its crown canopy. The 
competition of different species in a mixed stand and their ability to 
occupy space released by cutting, determines which of these species 
will benefit in form of increased growth. 



364 GROWTH OF TREES IN DIAMETER 

In order to predict growth of trees for any given set of conditions 
from a study of diameter growth of existing trees, it is necessary to select 
trees whose conditions of growth, for the past period measured, coincide 
as closely as possible with the conditions of site, density of stand and 
crown spread of the trees whose growth is to be predicted. Only in 
this .way can the excessive variability of diameter growth be averaged 
on a useful and accurate basis. 

Probably the greatest utility of the study of diameter growth is as 
an indication of the possibilities of management. Its direct relation 
to the crown, and its dependence on growing space make it an index 
of the results of thinning, spacing in plantations, and selection of trees 
for removal in mature stands. Maintenance of diameter growth 
throughout the life of a stand is the proof of successful intensive manage- 
ment. Since the rotation, or period required to grow timber, is indi- 
cated in part by the sizes or diameters of the trees which permits of 
their use for given products, the rate of diameter growth in imthinned 
versus thinned stands gives a direct indication of this rotation period, 
and is so used. 

References 

Some Suggestions for Predicting Growth for Short Periods, J. C. Stetson, Forestry 

Quarterly, Vol. VIII, 1910, p. 326. 
Accelerated Growth of Balsam Fir in the Adirondacks, E. E. McCarthy, Journal of 

Forestry, Vol. XVI, 1918, p. 304. 
Method of Taking Impressions of Year Rings in Conifers, L. S. Higgs, Forestry 

Quarterly, Vol. X, 1912, p. 1. 
Notes on Balsam Fir, Barrington Moore and R. L. Rogers, Forestry Quarterly, Vol. 

V, 1907, p. 41. 
Accelerated Growth of Spruce after Cutting, in the Adirondacks, John Bentley Jr., 

A. B Recknagel, Journal of Forestry, Vol. XV, 1917, p. 896. 
Notes on a Method of Stud^ying Current Growth Percent, B. A. Chandler, Forestry 

Quarterly, Vol. XIV, 1916, p. 453. 



CHAPTER XXV 
GROWTH OF TREES IN HEIGHT 

281. Purposes of Study of Height Growth. The rate of height 
growth in trees is desired in order to determine the relative abihty of 
different species in a mixed stand to survive and dominate their com- 
petitors. Height growth is the factor which largely determines the 
future composition of mixed even-aged stands. A condition of sup- 
pression is indicated by the diminution of height growth. Trees capable 
of living under suppression have the power of maintaining a much 
reduced height growth for a long period and of afterwards recovering 
and increasing this rate. In the second place, data on height growth 
are desired to determine the quality of site as a basis for classifying plots 
in the study of yields per acre for yield tables. The relative heights 
based on age which are attained by trees and stands are a close indica- 
tion of the site quality, even superior to volume production as a reliable 
index of site. Finally, height growth is deshed as a step in the deter- 
mination of the growth of trees in volume whenever the latter data are 
required. 

282. Influences Affecting Height Growth. Species. The juvenile 
period following germination (§ 257) is followed by a period of rapid 
height growth which is maintained until the tree has reached from 
two-thirds to three-fourths of its total maximum height. This period 
is coincident with the rapid reduction of numbers in an age class and 
with the expansion of the crowns and the elimination by suppression 
of those trees which are unable to maintain their position and crown 
spread in the stand through being overtopped. 

The third period is marked by increasing slowness and finally by 
practical cessation of height growth and a marked change in form of 
crown. In some hardwoods this is the result of division of the main 
stem into several branches, and in conifers it is characterized by the loss 
of the habit of producing annual whorls of branches. This habit, 
however, is retained by many species such as spruce and fir. When 
the power to produce annual whorls is lost, the growth in height becomes 
similar to that of branches. The power of recovery of height growth, 
which has been retarded or suppressed, is lost at an early age in intoler- 
ant species, but with tolerant species may be retained for a long period. 

365 



366 GROWTH OF TREES IN HEIGHT 

Unless trees can maintain a satisfactory continuous rate of height 
growth individuals so stunted never attain the full height and form 
of an average mature tree. 

The rapidity of height growth and the total heights ultimately 
attained are a specific characteristic which is retained whether the 
species is growing in mixture with other species having different rates 
of height growth, or in pure stands. Competition of faster growing 
species does not serve to stimulate the rate of height growth of a species 
to an appreciable extent. Height growth plays an important role in 
the survival, dominance and suppression of competing species. 

Quality of Site. The height growth of trees and stands is dnectly 
affected by the quality of the site, to such an extent that the rate of 
growth of trees in height, and the total heights attained serve as the 
most reliable index for determining differences in site qualities and 
formulating a basis of classification for sites. This relation between 
height growth and site quality is largely independent of one of the factors 
which influence diameter growth of trees (§ 270) namely, density of 
stand. Although in some species, especially hardwoods with deliques- 
cent stems, total height attained is less for open-grown trees than for 
crowded trees, this is not always the case and the rate of height growth 
is usually retained. On the other hand, stands, especially of conifers, 
which are so densely stocked as to lead to stunting and starvation, 
will show a decided loss of height growth. One instance is recorded 
in which a stand of lodgepole pine 70 years old containing 70,000 trees 
per acre, had attained a height of but 10 feet. 

The law of height growth of trees in a stand is to maintain as far 
as possible an even rate of growth for all the trees in an age class or crown 
canopy. There is considerable differentiation between trees with 
dominant, intermediate and overtopped crowns, the individual rate 
of height growth decreasing progressively with the loss of vigor and 
dominance of the crown; but this differentiation is constantly dimin- 
ished for the surviving trees in an age class by the death of the over- 
topped trees whose rate of height growth has slowed down. 

When the growth in height for stands is measured, it is gaged by 
the growth of dominant or sub-dominant trees, which gives very con- 
sistent results. By thus eliminating the effect of crown class, height 
growth of stands becomes almost directly an expression of species and 
of site quality. 

Crown Class ana Suppression. The influence of shading, which 
kills overtopped trees in an even-aged stand, also has a very marked 
influence on height growth of trees of an age class growing under sup- 
pression or in the shade of older trees. The normal rate of height 
growth is checked by shade, and if it does not result in death the tree 



RELATIONS OF HEIGHT GROWTH AND DIAMETER GROWTH 367 



survives with so greatly reduced a rate of growth in height that this 
rate is no indication of the capacity of the species nor of the quahty 
of the site. Normal heights, both as to growth for a current period 
and total height attained at a given age, can be determined only for 
trees which have grown throughout their life cycle free from suppression 
or overtopping. 

283. Relations of Height Growth and Diameter Growth. Although 
both growth in height, and growth in diameter, are responsive to site 
quality, they follow different laws in response to density of stand and 
crown class. As the result of the tendency for all trees in even-aged 
stands of intolerant species either to maintain the average height growth 
of the stand or to die, the relation between diameters and heights for 
individual trees is not consistent. The diameter growth of dominant 
trees is relatively faster than the height growth, while the height growth 
of the trees in danger of being overtopped, although a little slower than 
that of these dominant trees, is still relatively faster than their diam- 
eter growth which falls off in proportion not to height but to spread 
of crown. For this reason a dominant tree of a given height will be a 
stout tree with low form quotient (§ 171) while a suppressed tree in 
the same stand will be slender and cylindrical. 

These relations are emphasized when trees of different stands are 
compared on the basis of diameter. Dominant trees of a given 
diameter will be comparatively short, while suppressed trees of this 
diameter will be 
tall and slender. 
When the ages 
of these trees are 
compared, the 
short dominant 
tree is found to 
be a young tree, 
compared with 
the suppressed 
tall tree, which is 
much older. 

These rela- 
tions between 
height and diam- 
eter of stands ^^^^ ye.— Heights of trees based on diameter in three even-aged 
stands compared with heights of dominant, intermediate and 
suppressed trees of different diameters. 



















/ 








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60 

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Diaractcrn.il. Inches 



and trees are 
shown in Fig. 76. 
Within a given 
age class, the curves indicate the somewhat slower growth in height 



368 



GROWTH OF TREES IN HEIGHT 



of Ihe suppressed trees, but the maintenance of nearly the average 
rate for all surviving trees. But the dotted lines indicate the greater 
height of suppressed trees having a given diameter, when compared 
with dominant trees. 

284. Measurement of Height Growth. For the juvenile period of 
height growth of seedlings and saplings a practical method of measure- 
ment is to determine the total 
age and the total height of 
dominant trees (§256 and §257). 
Trees which will not survive 
should not be measured for 
height. For young conifers show- 
ing annual whorls, the exact 
height growth for each year may 
be determined by measuring the 
length of the whorl. This method 
is used in measuring the annual 
height growth of coniferous plan- 
tations (§ 258). 

On older trees height growth 
should be measured by analyzing 
the growth of individual trees. 
Total height growth for a given 
tree is obtained when its height 
and total age are known, and a 
composite growth cm-ve may be 
built up as suggested for seed- 
lings, by obtaining these data for 
a number of trees of different 
ages on the same site quality, 
plotting the heights on the basis 
of age and drawing an average 
curve of height on age. But a 
more accurate method is possible 
when each tree has .been cut into 
several sections, the age of which 
can be determined from ring 
counts. In this case as many 
points for a curve of height 
growth are found as there are 
sections cut, and these points 
form a true growth curve for the tree. Diameter growth begins, at 
a given section, in the year in which the tree reaches the height of this 



(1) 

Kings 
in 

Section 


(2) 

Height 
of 

Section 
Foct 


(3) 

Length 
of Log 

Feet 


(4) (5> 

Years to Years to 
Grow in Grow- to 
height height o) 
for Log Section 






53 




70 




















16 


" 




26 


37 


,f 


\ 


44 




33 


33 






37 






\ 


in 


OC 




\ 










f 


7 






54 


17 






16 












8 


4 






68 


9 






12 










1 J. 


r 


M 


\ „ 




70 


^ L 


1 


3 1 \ " 




Age 
Age 


of Seedling, 3 Years 
ofTree] 70 Years 

1 1 



Fig. 77. — Method of determining the 
growth in height of a tree from the 
ages of upper sections, or ring counts. 
The difference in age between consecu- 
tive sections indicates the period re- 
quired to grow in height from the lower 
to the upper section. 



MEASUREMENT OF HEIGHT GROWTH 



369 



section. The number of rings shown by the section, when subtracted 
from the total age of the tree (age of stump plus seedling age) gives 
the years required to grow to this height. The process as shown in 
Fig. 77 consists of the following steps : 

1. Determine age of tree from stump plus seedhng age (§ 257). 

2. Count the rings at each successive upper section, and measure 

length of section to get height from ground. Include 
height of stump. 




■10 
Age, Years 

Fig. 78. — Alternate methods of averaging the heights of trees, for a curve of height 

based on age. Original data plotted. For curve average age 

at fixed heights is found. For curve © average height for each decade. 

The prolonged curve is made necessary by dropping out of fast-growing 

trees from the average by decades. 

3. Subtract these counts successively from total age of tree, to 

obtain total height growth at each section and age. 

4. Subtract the age of any section from that of the one below, 

to find the period required for the current growth in 
height for the length of section. 

This method may be simplified by first computing the height growth 
curve for the portion above the stump, on all trees, and afterwards 
making the average correction required for stump height and correspond- 
ing age of seedling, on the final curve or table. 



370 



GROWTH OF TREES IN HEIGHT 



Graphic Method. In averaging together the data for height growth on the basis 
of age, it is evident that few if any points will fall at the same age, even if taken 
at the same height above groimd. For this reason, the most convenient method of 
determining an average rate of height growth based on age is to plot the original 
data for each tree, and draw a curve based on ocular inspection of the result assisted 
by weighting the points or calculating the position of the average point if the data 
are not sufficiently abundant to dispense with this step. In this graph, age is placed 
on the horizontal scale and height in feet on the vertical scale. 

It is not practicable to determine the arithmetical average height at each separate 
age previous to plotting the data. This is best done from the graph. The height 
growth of ten trees, which were sectioned at 8-foot intervals above the stump 
is shown in Fig. 78. Stump height is omitted. The heights at each 8-foot section 
fall on the same horizontal line, i.e., have the same ordinate. The total or final 
heights represent the height of the tree. 

Two methods of averaging the data are shown. By the first, all points falling 
in the same decade are averaged for the points marked O. The number of points 
used is indicated at base of Fig. 78. This method is based on age, but in some decades 
the same tree enters twice while in others it does not appear. The depression of the 

curve at final decade is caused by 
the dropping out of eight of the ten 
trees from the average. 

The second method is to aver- 
age the age at each 8-foot point. 
This average, marked <S>, is then 
based not on age but on height, but 
is plotted on age. Since all ten trees 
enter this average at each of three 
points, the curve is more regular 
than the first. There is not the 
same objection to interchanging the 
basis of this curve between age and 
height as outlined above, as there 
is in studying diameter growth, 

*" since the rate of height growth 

Fig. 79.— Method of correcting curve of height ^^^ ^^^^ ^^^^.^ ^^ ^^ ^^^^ ^^^_ 

growth based on stump, by adduig height gi^^ently a function of age and vice 
and age of seedling, thus givuig height ^^^^^^ j^^. ^j^^ ^^^^ ^^^^-^^ ^j ^j^.^^ 
growth of tree based on its total age. ^j^-^g j^j. diameter growth two or 

more additional variables influence the rate of growth (§ 296 and § 270). 

The height growth, as read from the above curve, may be shown in a table based 
on total age and height of tree, by adding average stump height (of 1 foot), and seed- 
ling age (of 2 years) to the curve, and reading the corrected values from the pro- 
longed curve, as shown in Fig. 79. 

The values, read for even decades are given in Table LVII: ' 

1 The averaging of the above data to obtain the weighted average points may be 
simplified, after the points are plotted, by the following method. For the first 
decade, average heights include 7 trees, each 8 feet or points above the base of the 
graph, or " up " and 1 tree 16 feet " up " or a total of 72 points " up"; average for 
8 trees, 9 points " up." Average age includes 3 trees 4 years or points to right of 
the left margin of the graph, or " over," 2 trees 5 years " over," 1 tree 6 years, 1 
tree 7 years and 1 tree 8 years, a total of 43 years, average 5.4 points " over," These 































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- -X - 






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7' 






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20 


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1 1 1 1 1 N 1 — 



MEASUREMENT OF HEIGHT GROWTH 



371 



TABLE LVn 

Height Growth of Chestnut Oak, Milford, Pike Co., Pa. 

Basis, Ten Trees 



Age. 


Height. 




Height. 


Years 


Feet 


s 


Feet 


2 


1 


40 


35 


10 


10 


50 


41 


20 


19 


60 


46 


30 


28 


70 


50 



The total height, based on total age, of these ten trees is shown by the last ten 
points. It is evident that with a sufficient number of trees of all ages, a height curve 
based on age could be constructed without analyzing the trees above the stump sec- 
tion, but it is equally evident that such analyses, as shown in the figure, not only 
multiply the weight of each tree by the number of sections taken but substitute 
actual growth of given trees for composite growth by comparison of different trees. 
Such a history or record of growth, whether it is of diameter, height or yields per acre, 
(§ 266 and § 326), is the most reliable basis of growth data. 

Current HeigM Growth. The current or periodic height growth 
for the last decade or two may be required to complete the data for 
determining the current volume growth of trees. This should be meas- 
ured on felled trees by cutting back the tip until a section is found 
containing the requh'ed number of rings. For determining growth 
for short periods this is a simple process. Only on young trees should 
the last period of growth be determined by counting back the number 
of whorls from the tip In older timber and especially on standing 
trees, it is impossible to secure accuracy by this method. 

285. The Substitution of Curves of Average Height Based on 
Diameter for Actual Measurement of Height Growth. In studies 
intended to determine the volume growth of trees, especially of seed 
trees and young timber left on cut-over lands, a method has been sought 

data are identical with the original figures, the advantage lying in the graphic classi- 
fication of the data for averaging. But for the next and subsequent decades the base, 
for age, can be shifted to the right by one decade, so that the points " over " include 
only the fractional decade, while for height the base can be raised to exclude that 
portion of the graph which includes no points. Thus, for the third decade there are 

9 points, whose weights vary from 1 to 10 years or points. For age, the basis or 
zero is 20 years and the points " over " are 1, 2, 3, 6, 6, 7, 8, 9 and 10, or a total of 
52, average 5.8 points " over " or 25.8 years. For height the base may be taken at 

10 feet and the points " up " are then 6, 14, 14, 14, 22, 22, 22, 22, 30, a total of 166 
points " up," average 18.4 points up, or 28.4 feet. In plotting, where two or more 
dots fall on the same point, a numeral miist be written in, as indicated, to show the 
weight of the point, 



372 GROWTH OF TREES IN HEIGHT 

by which this volume growth can be predicted by a study of diameter 
growth and by the determination of the resultant volume of the tree 
from its average height and volume as shown in a volume table. In 
order to save the expense of determining the actual growth in height 
of these trees, recourse is had to the relation between height and diam- 
eter as expressed by a curve of heights based on diameter such as is 
illustrated in Fig. 76. The process is as fo lows: 

1. The increase in diameter for a given period for a tree of a certain 
diameter is predicted or determined; e.g., the tree may gi'ow from a 
10-inch to a 12-inch diameter. 

2. The average curve of height on diameter shows the heights of 
a 10-inch and 12-inch tree respectively. 

3. It is then erroneously assumed that the 10-inch tree will grow 
in height by the amount of this difference, that is, that it will have, 
when 12 inches in diameter, the height of a 12-inch tree. The fallacy 
of this reasoning is clearly evident when applied to any single tree or 
to any stand of a given age. If the tree or stand is young and the curve 
of height on diameter has been prepared for trees of this class or age 
in the vicinity, the tree will grow much faster than the difference in 
height indicated by this curve, and the same is true of the trees in an 
even-aged stand. But for old or mature even-aged stands, the reverse 
may be true and the trees may grow more slowly than the difference 
shown. Such a curve is not a growth curve at all, but a curve showing 
the average heights attained by trees which may be all of the same 
age. Only when the curve of height based on diameter includes trees 
of all ages as well as diameters, does it approach the form of a true 
growth curve, as shown by the dotted curves in Fig. 76. To do this 
it must harmonize two variables, namely, diameter and age. In general, 
small trees are young trees and large trees are old trees. If sufficient 
data have been included, covering wide enough ranges both of diameter 
and of age, and the measurements are taken on the same site quality, 
a rough average is obtained in which the height of a tree of given diam- 
eter is correlated with the age of tree of the same diameter. The more 
nearly this general result is obtained, the more reliable will be the aver- 
age results of applying this curve in predicting the growth in height 
through the medium of the growth in diameter to trees or stands of all 
ages, and thus avoiding a direct study of height growth. It is obvious 
that for special problems on specific classes, ages and stands of trees, 
no such generalized curve should be depended upon, but a few measure- 
ments of height growth on the trees in question will give results whose 
a(;curacy justifies the expense. 

The height curve of even-aged stands is determined either from the 
height growth of the maximum or dominant trees in the stand, or from 



REFERENCES 373 

that of trees containing the average volume of the stand. It has been 
found that the relation between dominant and average trees in height 
growth is very consistent, and either basis furnishes an index to the 
growth rate, which may be used later in classifying the plots on a basis 
of site for the construction of yield tables. 

On account of its uniformity for a given site quality, average height 
growth may be determined from the analysis of from five to twenty- 
five average or dominant trees with very satisfactory results. 

References 

Relation between Spring Precipitation and Height Growth of Western Yellow Pine, 

G. A. Pearson, Journal of Forestry, Vol. XVI, 1918, p. 677. 
Relation between Height Growth of Larch Seedlings and Weather Conditions, 

D. R. Brewster, Journal of Forestry, Vol. XVI, 1918, p. 861. 



CHAPTER XXVI 
GROWTH OF TREES IN VOLUME 

286. Relation between Volume Growth, Form and Diameter Growth. 

The growth of trees in volume is the product of the growth in height 
and the growth in area at different portions of the stem, which Is 
expressed in diameter growth. The exact form of the tree and the rela- 
tion between diameter and resulting area and volume growth at dif- 
ferent heights from the ground are the result of mechanical laws of 
resistance to stresses. The form of the tree is intended to resist wind 
pressure in order to maintain its upright position and not be snapped 
off or blown over. As was shown in Chapter XVI this pressure is 
directly caused by the force of the winds acting on the crown and 
focused in the center of area of the crown exposure (§172). Growth 
in diameter will be distributed in response to this strain to give the 
maximum resistance with the minimum of material. 

As the form of crown and its position with respect to the bole changes, 
the point of average pressure shifts and the form of the tree will be 
modified by a more rapid diameter growth at the points requiring 
strengthening. An increase in the stress to which the tree is exposed 
will also cause changes in the distribution of growth. Trees which 
have grown in a protected stand and are exposed by cutting will either 
blow over or will rapidly strengthen their resistance by laying on 
increased growth at the base or stump where the effect of this change 
in exposure is most evident. The upper form of the tree, being influ- 
enced by crown, does not change appreciably. Trees in a leaning 
position continually add most of the diameter growth on the under side. 

Where the growth in volume of a tree on cut-over areas is judged 
from the growth in diameter on the stump, without correction, a rate 
of from 50 to 100 per cent in excess of the true volume growth may be 
obtained. Such measurements should therefore be taken at B.H. 
where the effect of this increase is not felt, or else growth measurements 
taken on the stump must be carefully compared with measurements 
at upper points on the tree. 

287. Tree Analysis, its Purpose and Application. The analysis of 
an individual tree by the measurement of diameter growth at upper 
sections, in order to determine its volume growth, is termed tree analysis, 
(synonym, stem analysis, § 254). This process enables one to determine 

374 



SUBSTITUTION OF VOLUME TABLES FOR TREE ANALYSIS 373 

the upper dimensions and volume of trees of a smaller size than those 
which exist in a given stand. This is an advantage in case such 
smaller sizes are lacking, but where present they may be directly meas- 
ured. The volume which trees produce at given ages can thus be 
obtained in one of two ways, either by measuring trees of different 
ages directly for volume or by analyzing a single tree or a number of 
trees in order to determine the past growth in volume. The latter 
method alone will bring out the changes which take place in form, as 
described above, due to altered conditions. In applying such growth 
figures to answer the fundamental question of growth studies, namely, 
what is the rate of growth in volume per acre, annually or for a given 
period, not only must the growth of average rather than individual 
trees be determined, but the relations of these average trees to the 
number of trees which will survive on an acre at different ages must 
also be known (§ 275). Since the recording and working up of growth 
measurements to determine total volume growth is slow and expensive, 
only a few trees may be taken. It is necessary that these trees have 
the average form quotient for the stand to which their results will be 
applied. This means either a careful selection or a chance of incurring 
an error of from 10 to 15 per cent by the accidental selection of trees 
which depart from this average in form. 

288. Substitution of Volume Tables for Tree Analysis. The growth 
of an average tree is determined by the average growth in D.B.H., 
the average height growth and the average growth in diameter at 
upper sections, of which the most important is the diameter growth 
at one -half of the height. The growth of upper diameters is usually 
accompanied by a change in form, caused by a change in the length and 
position of the crown. This is illustrated in Fig. 80 (§ 290) for 
which tree both butt swelling and upper diameters increased faster 
than growth at 8 feet. 

Relying upon the maintenance of a consistent tree form for average 
trees, a method is in common use as a substitute for the analysis of 
trees to determine their volume growth. This method depends upon 
the use of volume tables to determine the volume of trees whose height 
and diameter are known. Since a standard volume table expresses 
the actual volume of average trees much more accurately than it can 
be obtained by the analysis of a few sample trees, the substitution 
of a volume for the average tree taken from this table enables the investi- 
gator to concentrate his effort on determining average growth in D.B.H. 
and in height. The actual measurement of height growth involves 
the counting of rings for determination of age of upper sections on at 
least a few trees (§ 284), but dispenses with the measurement of diameter 
growth on these upper sections, and requires from one-fifth to one-tenth 



376 



GROWTH OF TREES IN VOLUME 



as many trees as are required for the study of average diameter growth 
on account of the greater consistency of height growth based on age. 
From a curve of growth in diameter, based on age (§ 267 and § 268), 
the diameters of the average trees at different ages are determined. 
From a second curve of height based on age (§284), the heights of the 
same average trees for different ages are found. Since diameter and 
height determine the volume as classified in these standard volume 
tables, the requisite volume is interpolated from the values in the table 
for the nearest yV-inch in diameter and foot in height. The successive 
volumes found in this way indicate the growth laid on by the average 
tree. This may be expressed in whatever unit of volume is represented 
by the volume table employed. This method is almost universally 
substituted for volume growth analysis wherever figures on average 
volume growth of trees are desired. This method is illustrated by 
Table LVIII.i 

^ The method of interpolation is illustrated as follows. The 60-year-old tree is 
6.6 inches in D.B.H. and 46 feet high. The values in the standard table from 
which to interpolate are, in cubic feet. 



D.B.H. 

Inches 


Heights 


40 Feet 


50 Feet 


Cubic Feet 


6 

7 


4.2 
5.7 


5.0 
6.6 



The difference for 1 inch is 1.5 cubic feet for 40-foot trees, and for .6 inch, is 
.9 cubic foot, giving for 6.6 inches, 5.1 cubic feet. The average difference between 
40- and 50-foot trees is .85 cubic foot. For 46-foot trees it is .6 times .85 = .51 cubic 
foot. Then 5.1 + .51 =5.61 roimded off to 5.6 cubic feet as the interpolated volume 
sought. These interpolations are more expeditiously made from graphic plotting 
of the values in the volume table. 

One drawback to the use of volume tables as a substitute for actual growth analy- 
sis is illustrated in the attempt to measure growth at successive decades on sample 
plots for scientific purposes. Even here, if a single volume table is carefully pre- 
pared, combining all age classes, the transition in form from young to old trees is 
blended with the volumes shown in the table for small and large trees, but where, as 
for instance with Western yellow pine, separate volume tables were made for black 
jack or young trees and for yellow pine or old trees which differed by about 10 per 
cent in the average volume due to difference in form, the application of a different 
volume table to trees passing from one age class to the other caused a jump of 10 
per cent in the volume due apparently to growth, but in reality due to the irregular 
distribution of this growth by separation of form classes in these tables. 



MEASUREMENTS REQUIRED FOR TREE ANALYSES 



377 



TABLE LVIII 

Growth of Chestnut Oak 
In Cubic Volume, from Diameter and Height Growth and Use of a Standard 

Volume Table 









Corresponding * 










volume from 


Periodic 


Age. 


D.B.H. 


Height. 


table by 
interpolation. 


growth. 


Years 


Inches 


Feet 


Cubic feet 


Cubic feet 


10 


1.2 


10 






20 


2.5 


19 






30 


3.8 


28 


1.3 . 


1.35 
1.55 
1.40 
1.40 


40 


5.0 


35 


2.65 


50 


5.9 


41 


4.2 


60 


6.6 


46 


5.6 


70 


7.2 


50 


7.0 ' 



* Cubic volumes taken from Frothingham's table for chestnut oak in Bui. 90 Forest Service, 
"Second Growth Hardwoods in Connecticut." Height from Table LVII, §284. Diameter from 
growth of the same ten trees used in this table. 



40 



185 



10 



\ 












}\ 


10 y 


ears 










\ 
\ 


\ 










7\ 


10 \ 


\' 


1 






\ 






1 


10 \ 


,\ 


24 y 


lars 




} 






I 


\ 








ho 


\. 


Ml 


Mil 




^ 




V.N 


fX 


5. 


6 ) 


10 


k 


10 \io\ 


^-y 

























12 3 4 5 6 
Diameter, inches 



Fig. 80. — Stem analysis of a 
tree 36 years old, by dec- 
ades, counting in from 
outer ring, based on stump. 
Stump is shown below 
point marked 0. 



289. Measurements Required for Tree 
Analyses. The data required in a tree 
analysis, in addition to those taken for 
volume and itemized in § 134 and § 135, 
are, 

1. Age of each section (height above 
stump and length given). 

2. Growth on average radius from center 
to outer ring, by decades. 

3. Where needed, width of sap and 
number of rings in sapwood. 

290. Computation of Volume Growth for 
Single Trees. The method of computing 
the growth in volume for a given tree is 
best shown by graphic illustration. Fig. 
80 shows the dimensions of a chestnut oak 
36 years old at the stump, and the size 
which this tree had when 26, 16 and 6 
years old. 

To correlate the growth of upper section 
for the same decades, these decades are 
counted from the circumference inward, as 
shown, with the odd rings at the center. 
Diameter growth for each decade is then 



378 



GROWTH OF TREES IN VOLUME 



measured from center outward, 
are given in the following table : 



The full data for this tree analysis 



TABLE LIX 

Stem Analysis of a Tree 



Species, Chestnut Oak. 
Date, 1912. 
Total Height, 40 feet. 
Width Crown, 14 feet. 
Tree Class, Suppressed. 



Locality, Milford, Pike Co., Pa. 
D.B.H., 4 inches. Height Stump, 1 foot. 
Merch. Length, 20 feet. 
Length Crown, 17 feet. 





Height 


Length 


Diameter, 


Width 


Diameter, 






above 


of 


outside 


bark. 


inside 


Age. 




stump. 


section. 


bark. 


single. 


bark. 






Feet 


Feet 


Inches 


Inches 


Inches 


Years 


Stump 





1 


6.05 


0.5 


5.05 


36 


1 


8 


8 


3.95 


.3 


3.35 


31 


2 


16 


8 


3.5 


.2 


3 1 


24 


3 


24 


8 


2.3 


.15 


2.0 


17 


4 


32 


8 


1.0 


.05 


.9 


10 


Tip. 


39 


7 











Distance in inches on average radius from center to ring, by decades. The 
first column shows the number of years in the first fractional decade. 





(1) 


(2) 


(3) 


(4) 


(6) 


0.5 


1.3 


2.1 


2.5 


(1) 


0.05 


0.65 


1.25 


1.7 


(4) 


0.25 


1.05 


1.55 




(7) 


0.55 


1.0 






(10) 


0.45 









In addition, for a group of trees analyzed, the site, density of stand, 
character of trees shown, conditions of cutting or other factors whose 
influence on growth is to be determined, are recorded. With diameter 
at each decade for each section recorded, the total volume of the tree 
and its volume at each decade in the past, e.g., for 36, 26, 16 and 6 
years, is obtained by methods indicated in Chapter III, using the 
Smalian or the Huber formula for cubic contents. 

But one detail is lacking — the actual height which the tree had 
at the above decades, in case the former tip falls between two of the 
sections counted. This tip contains a very small per cent of total 
volume, and for merchantable contents would be ignored. But for 
accurate studies of total cubic contents the height is obtained by assum- 
ing that the height growth maintained the same rate per year as shown 



SUBSTITUTING AVERAGE GROWTH IN FORM OR TAPERS 379 

for the entire section concealing the tip; e.g., in Fig. 80 the third sec- 
tion took 24—17 = 7 years to grow 8 feet. The tip contains 4 rings, 
or 4 years' growth. Hence its height is y of 8 feet = 4.5 feet. For the 
second section the period required was 31 — 24 = 7 years. The tip 
has 1 ring, hence its height is y of 8 ft. or 1.1 ft. or 

/ Age of tip \ 

Length of tip = I — 7 : -; — I Length of section, 

\ Years to grow length 01 section/ 

The age of any one tree will probably fall at an odd year instead 
of an even decade and the age of the average tree whose volume is 
calculated will fall on one of these odd years; e.g., for the chestnut 
oak above analyzed which took 2 years to grow to stump height, the 
table and figures above will show the age of a tree 8, 18, 28 and 38 years 
in age. To find the volume of the tree at even decades, as 10, 20, 30 
years instead of odd years, the volumes as determined are now plotted 
on cross-section paper on which age is placed on the horizontal scale 
and volume on the vertical scale. From these curves the volumes 
for even decades can be read. By averaging these volumes on the 
basis of age the average growth in volume is obtained for all the trees 
analyzed. 

291. Method of Substituting Average Growth in Form or Tapers, 
for Volume. The taper measurements or diameters determined from 
Fig. 80 thus enable one to ascertain the volume of the tree at different 
ages expressed in any unit. In this it does not differ from taper tables 
discussed in § 167 except that age is now the basis of the dimen- 
sions shown. 

The advantage of recordmg the tapers for the individual tree rather 
than its separate volumes at different ages applies equally to the average 
of a number of trees analyzed for volume growth. For this reason 
the method of computing volumes directly for each tree has given way 
entirely to the method described below by which the average tapers 
or dimensions of all of the trees studied are first determined. From 
the average tree thus plotted, the volumes can then be found for any 
of the desired units, such as cubic feet, board feet in any given log 
rule, standard ties or poles, for each age or decade. This method 
reduces the work of computing volumes to a single average tree for 
each tree class. 

The first requii'ement of this method is a curve of average growth 
in height based on age (§ 284). This establishes the year or age in the 
life of the tree at which the diameter growth of each upper section 
at a given height originates and marks the zero or origin of the curve 
for this section when plotted on the age of the tree (§ 269). Second, 
a separate curve of diameter growth based on age is constructed for 



380 GROWTH OF TREES IN VOLUME 

all sections which fall at the same height above the ground. The sum 
of the age or period required for the average tree to reach this height, 
plus the age or period represented by the growth of the section equals 
the age of the tree regardless of the height of section. It is evident 
then that the average curve of growth in diameter for any of these 
sections can be plotted on a single sheet of cross section paper whose 
horizontal scale represents the age of the tree and whose vertical scale 
represents the diameter of any cross section. A cross section which 
does not begin to grow in diameter for 17 years will diminish to zero 
and the curve representing its growth will intersect the base or zero 
diameter at 17 on the horizontal scale representing age of tree. 

In Fig. 70 (§ 269) a curve of stump diameter based on the age of the 
tree was shown as intersecting this base at the age represented by the 
seedling. On this same sheet a curve representing the D.B.H. and one 
showing the diameter at the top of the first 16-foot log were indicated 
with their points of intersection. On a single vertical line the points 
shown were the diameters of a tree of a given age and indicated the 
D.B.H. , D.I.B. at stump and D.I.B. at top diameter of first log for 
this age. But to get a curve showing these three dimensions for trees 
of different ages in the illustration given, the points were not taken 
from the growth of one tree, but by the measurement of several trees 
differing in age, stump diameter and corresponding D.B.H. and upper 
tapers. The connection of the points for these separate trees which 
differ on the basis of age, gives the curves showing the increase in the 
upper diameters or tapers for trees of different ages. 

The method of plotting the upper diameters showing the growth 
of an average tree at the different ages of its life is identical with this 
previous method, with the exception that instead of these ages being 
represented by the final, present or outer dimensions of separate trees, 
they include the past, interior dimensions as well, by the measurement 
of past growth. Even though the growth is an average of many trees, 
the method still remains the same since each decade's growth is a com- 
posite of the actual growth or internal dimensions of a number of trees. 
The method of plotting the data is as follows : 

1. Prepare and plot a curve of average height based on age on a 
separate sheet. 

2. Prepare on separate sheets, curves of average diameter growth 
for all cross sections falling at each separate height, as for instance a 
curve for sections falling at 8 feet, 16 feet, etc., including one for the 
stump section. It is assumed that the height of seedlings based on 
age has been determined and that D.B.H. has been correlated with 
stump D.I.B. 

3. After determining the initial or zero year for each of the curves 



SUBSTITUTING AVERAGE GROWTH IN FORM OR TAPERS 381 



of diameter growth, including the stump section, transfer or assemble 
each of these curves on a single sheet whose zero represents the zero 
year of the tree's age. 

In Fig. 81 the curve of stump growth from Table LIX is plotted 
with the zero at 2 
years, age of seed- 
ling of stump height. 
This is usually as- 
sumed to be also 
the origin of the 
D.B.H. curve. For 
the curve of diam- 
eter growth at 8 feet, 
the period required 
to grow to this 
height by Fig. 81, 
or by interpolation 
in Table LIX is 7 
years plus 2 years 
for seedling. The 
zero is placed at 9 
years. Since the 
first fractional dec- 
ade averaged 6 years 
on these sections, the 
first diameter is plot- 
ted above 9-|-6=15 years, and subsequent decades at 25, 35 years, 
etc., as indicated by the points. 

The height growth for section 3 at 16 feet took 15-|-2=17 years. 
The first fractional decade was 6 years. The points are plotted above 
23, 33, 43 years. In this way each upper section is plotted on the sheet 
representing the age of the average tree.^ 

To read this record for the purpose of determining the volume in 
any given unit for a tree of a given age, the dimensions of a tree of the 
required age fall in the vertical line intersecting this age. For instance, 
a tree 40 years old will have its diameter inside bark at the 16-foot 
cross section indicated in Fig. 81 as 2.4 inches. Reading upwards 
as the diameter increases, the next lower cross section has a diameter 
of 3.4 inches and D.B.H. is 4.8 inches. Since the height or distance 
between these cross sections cannot be shown on this diagram, but 















j^ 


> 














y 












A 


y 




/ 








'M 














A 


/A' 

.A 




/, 








/ 


// 


/ 
/ 


A 










/. 


// 





// 


'p/ 


^ 


* 


/ 


/. 


^ 


'A 


/ 


/ 







30 40 

Age, years 



60 



Fig. 81. — Diameters at 8-foot points, for an average tree 
at different ages, or growth analysis. Chestnut Oak, 
Milford, Pike Co., Pa. 



1 In the above figure, D. B. H. outside bark exceeds D. I. B. at stump up to 
about 7 inches. This frequently occurs on small thick-barked trees. 



382 GROWTH OF TREES IN VOLUME 

only diameter based on age, it is necessary to indicate upon the curves 
the height which each curve represents. 

This series of curves can be used only to determine the diameters 
at the definite points, as 8, 16, 24 feet, etc., for which curves have been 
drawn. It corresponds with Fig. 32 (§ 168) for taper curves. To 
obtain the growth in form for the tree at intervening points, these 
curves should be replotted in the form shown for a single tree, in Fig. 80. 

From the average tree thus shown, the growth by decades in any 
form or length of product can be directly computed, to any required 
diameter limit. ^ 

292. Substitution of Taper Tables for Tree Analyses. Just as the 
above method" substitutes the form of the average tree at different 
ages for the direct calculation of the volume at these ages, so it is pos- 
sible to go one step further and to substitute the entire form or taper 
of trees of different diameters, heights and ages, just as was done in 
Fig. 70 on the curve of stump diameter growth, for D.B.H. and top 
of first log. To make this substitution, the diameter and height of 
average trees are first determined for each decade in age. Second, 
from a table of average tapers, the form or taper of trees of the cor- 
responding diameters and heights are taken. This may be done by 
interpolation in case the required diameter or height falls between 
inch diameter classes or 5- to 10-foot height divisions expressed in taper 
table. The tapers thus borrowed are assumed to be those of the tree 
at the different ages. 

This method has the same advantages and drawbacks as the sub- 
stitution of the volumes from a volume table for the actual volume 
of sample trees as described in § 242. The average tapers are taken 
in. most instances from a much larger number of trees than could be 
analyzed for form at the different decades of their growth. These 
tapers therefore probably represent quite closely the average form of 
the tree of these sizes and ages. On the other hand, this average, just 
as for volumes, may depart from the actual average of the trees to be 
measured in case the data do not coincide in origin and the trees differ 
in average form quotient. 

The best check upon the accuracy of substitution of taper tables 
for tree analyses is to test the form quotient both of the taper tables 
and of the trees desired. A considerable departure in this form quotient 
indicates that the tapers do not represent the average sought. 

1 This method of graphic plotting of average growth in diameter at eaeh upper 
section was devised by A. J. Mlodjiansky (Measuring the Forest Crop, Bui. 
No. 20, Division of Forestry, U. S. Dept. Agr., 1898). The method of assembling 
all the curves on the same sheet was devised by H. S. Graves (Forest Mensura- 
tion, 1906, p. 295). 



REFERENCES 383 



References 



Difficulties and Errors in Stem Analysis, A. S. Williams, Forestry Quarterly, Vol. I, 

1903, p. 12. 
Pitch Pine in Pike Co., Pa., John Bentley, Jr., Forestry Quarterly, Vol. Ill, 1905, 

p. 14. 
Stem Analyses, John Bentley, Jr., Forestry Quarterly, Vol. XII, 1914, p. 158. 
A Simplified Method of Stem Analysis, T. W. Dwight, Journal of Forestry, Vol. XV, 

1917, p. 864. 
Mechanical Aids in Stem Analyses, E. C. Pegg, Journal of Forestry, Vol. XVII, 

1919, p. 682. 



CHAPTER XXVII 
FACTORS AFFECTING THE GROWTH OF STANDS 

293. Enumeration of Factors Affecting Growth of Stands. The 

rate of growth per acre or total volume production of stands is the result 
of five classes of factors, namely, site, form, treatment, density, and 
composition. 

Under site are included all factors of local environment such as soil, 
exposure and altitude, which influence growth (§ 294). 

The term form alludes to age, and the forms of stands distinguished 
in yield studies are even-aged and many-aged (§ 259). 

Treatment refers to the silvicultural management of the stand, 
in the form of thinnings, and protection; untreated stands are those 
gi'own under natural conditions (§ 300). 

Density means primarily the completeness of crown cover, but this 
factor is also influenced by the number of trees per acre (§ 301). 

Under composition, pure and mixed stands are distinguished. Pure 
stands are those in which a single species comprises 80 per cent or more 
of the volume. Mixed stands are those made up of two or more species, 
none of which amounts to 80 per cent of the volume. Stands may be 
alluded to as pure if 80 per cent or more is composed of trees of the 
same genus, such as pure pine or pure oak stands. 

Natural enemies such as insects and fungi, and climatic factors 
such as tornadoes and ice storms reduce the density of stocking and 
lower the rate of growth, thereby widening the gap between average 
and fully stocked stands. 

294. Site Factors, or Quality of Site. In estimating the volume 
of stands, the forest type is made a distinct unit of area for the purpose 
of increasing the probability of accuracy in obtaining an average stand 
per acre, or in securing a curve of average height on diameter (§ 225 
and § 227). In the measurement of growth and yields, not only is 
the forest type also a fundamental factor, since it determines the 
species and composition of the stand, whose capacity for growth under- 
lies the results obtained, but these types must be further subdivided 
into site classes. 

The rate of growth per year or total yield for a given period for 
different species depends directly upon the combination of factors 

384 



VOLUME GROWTH A BASIS FOR SITE QUALITIES 385 

which influence this growth, chief among which are qiiahty and depth 
of soil, average moisture contents, slope and exposure, altitude and 
climate. Site factors cause a variation in total possible yields of from 
200 to 300 per cent. Hence for a given stand or area the jaeld cannot 
be predicted within a reasonable degree of accuracy unless the quality 
of site is taken into account. This difference in yield on good and on poor 
sites is caused by the more rapid growth in height, diameter, and volume, 
of the trees in the stand, when growing on more favorable sites. Fewer 
trees may mature on good sites than on poor, because of the larger 
sizes and crown spread attained, but the sum of their volumes will 
exceed those of the trees maturing on the poorer sites. When the 
period of years required to produce these yields is considered, and the 
mean annual growth is computed (§ 245) it will be seen that the more 
rapid growth on good sites produces even more striking differences in 
the annual rate of growth between poorer and better sites. These 
differences are further increased when the value of the yield is compared 
with the cost of production, so that it becomes of utmost importance 
in forestry to determine, for any large area of forest land, the acreage 
embraced in each of several grades or qualities of site. 

295. Volume Growth a Basis for Site Qualities. Forest types some- 
times show abrupt transition from one to another, corresponding to 
sharp differences in soil moisture; but more often the change is gradual 
and the separation of areas in each type, as made in the field, is arbitrary. 
The differences in site quality within a type form an unbroken series 
of gradations, which must be separated, on a purely arbitrary basis, 
into a convenient number of site classes, whose average yields may 
be expressed in tables. In European practice five qualities are recog- 
nized when a few species occupy a wide range of conditions. In America 
three qualities have so far sufficed to cover the range of a single species. 

The problem of classifying site qualities is two-fold. First, the 
plots whose yields are measured to determine the average rates of 
growth for different sites must be separated into the predetermined 
site classes. Second, some convenient means must be found to apply 
this site classification to forest lands during a forest survey in order 
that the total area may be subdivided on this basis for the prediction 
of growth on the forest. 

The most direct method of classifyin,g plots measured for yield is 
by the rate of growth per year actually produced, i.e., the total yield 
based on age of the stand. This has been the basis of most of the yield 
tables constructed in America, and might suffice were it not for the 
four other factors which modify the yields per acre independent of site; 
namely, form of stand, treatment, degree of stocking, and composition 
of stand. 



386 FACTORS AFFECTING THE GROWTH OF STANDS 

The influence of these variable factors is tremendous, and it has 
usually been considered necessary to eliminate them by constructing 
yield tables for given fixed conditions only, such as for even-aged 
stands, artificially grown and thinned, of normal or full stocking, and 
of pure species. Where these conditions do not apply, as for instance 
in mixed stands of broken density in forests of all ages, it has often 
been considered impossible to determine the rate of growth per acre. 

296. Height Growth a Basis for Site Qualities. A' though it may 
be possible, by rigid selection, to eliminate these four variables and thus 
base the site qualities upon the rate of growth or the total yield per acre 
based on age, yet when it comes to reversing the process and applying 
this standard of site classes to the classification of lands on a larger 
area, the remaining variables are present and must be dealt with. 
This problem may be summed up as follows: 

1. The factors of site, such as climate, and soil, are too complicated 
to be directly measured in the field as a means of site classification. 
Results expressed in forest growth, rather than causes, must be used 
as the indicator of site. 

2. Volume as a site indicator is incomplete without the determina- 
tion of age. For most conditions the relative volume based on age 
is too variable and difficult of determination to serve as a field basis 
of classification of large areas. 

3. Dimensions of typical dominant trees in a stand may serve as 
the required indicator, since the tree unit is independent of the variables 
of age, form, composition and density which affect the stand. 

4. The dimensions which may serve for this purpose are diameter 
and height. Of these, height alone is a reliable index of site quality 
since it is affected but little by varying density or degree of stocking, 
or by the treatment of the stand. Height based on age is a more 
reliable basis than volume on age for stands of varying degrees of stock- 
ing, and for both wild or unmanaged forests and thinned or managed 
stands. This reduces or eliminates two of the five variables, namely, 
treatment, and density of stand. Height growth is retarded by shade 
to a marked degree; hence in forests of all ages, and in mixed stands 
of several species, height based on total age ceases to be a reliable 
index, since the factor of economic age is introduced. 

Total height or height at maturity remains, even in mixed stands, 
a distinguishing characteristic of different site qualities. The growth 
of dominant, unsuppressed trees, a few of which may be found in almost 
every stand, may be ascertained in a very few tests and will hold good 
for the stand or site. Thus the remaining two variables, form and 
composition, may be eliminated by selection of dominant trees or fully 
mature trees. 



OTHER POSSIBLE BASES FOR SITE QUALITIES 



387 



Site qualities, whether three or five in number, must be adapted 
to the range of actual j^ields of the species to be measured. Different 
species require a different range of site factors. The conifers thrive 
in soils too poor for hardwoods; hence quality I for pines may be quality 
II for oaks. 

The adoption of a common standard of site index for species with the 
same range of soil requirements is desirable. One suggestion is to 
classify the trees of the country into groups, based on their total growth 
in height at a definite age. This principle is illustrated by the follow- 
ing table, in which four site classes are made for each group, based 
on even gradations of total height for dominant trees of the same age. 

TABLE LX 
Standards of Site Classification Based on the Height of Tree at 100 Years 



Site 


Standard a. 


Standard h. 


Standard c. 


Feet 


Feet 


Feet 


I 


110 


90 


70 


II 


90 


75 


60 


III 


70 


60 


50 


IV 


50 


45 


40 



A standardization of this character serves the double purpose of 
coordinating the yield tables for species of similar growth habits, and 
furnishing the simplest basis for site classification during forest survey. 

297. Other Possible Bases for Site Qualities. Medwiedew's Method. A 
method of site classification suggested by Medwiedew, a Russian, and appHed by 
Hanzhk to Douglas fir is as follows : 

A site factor is calculated by the formula, 



Site factor = 



cXh 



when c = basal area on the average acre ; 
h = average height of stand ; 
n=age of stand. 

These so-called site factors may then be grouped to represent different site 

qualities, all factors falling between certain limits indicating quality I, etc. This 

basis is not consistent as an indication of site, since it is nothing but the mean annual 

growth of the stand in a different form. If / = form factor, then, c/i/ = total cubic 

chj 
volume, and — = mean annual growth of stand. As mean annual growth varies 
n 

with age as well as site, it cannot be substituted for either volume or height as an 

absolute basis of classification. 



388 FACTORS AFFECTING THE GROWTH OF STANDS 

A still more impracticable plan is to base site factors on the current annual 
growth of a stand. ^ 

298. The Form of Stands. Even-aged versus Many-aged. There 

is an essential difference in the character of even-aged stands and those 
composed of all ages on the same area, and this difference constitutes 
one of the greatest difficulties in determining the rate of growth or yields. 
It has been shown (§ 274) that the competition between individual trees 
made necessary by the expansion of their crowns and growing space 
occurs in an even-aged stand between trees of the same age class. Except 
around the borders of this age class there can be no expansion of the 
areas occupied by the total stand belonging to this age class. The 
factor of area can therefore be standardized in yield tables. Since 
the yield of even-aged stands is composed of the volumes of trees which 
have remained dominant throughout the life of the stand, the rate of 
growth of the individual trees is a maximum both in height and diameter 
and the mean annual growth resulting on an acre is the maximum for 
the site when measured for the period required for the growth of the 
average tree from seedling to maturity. 

The conditions are entirely different in many-aged stands, the dif- 
ference being greatest for species which may be subjected to a long 
period of suppression and yet retain the power to survive and recover. 
In these stands several different age classes are brought into competi- 
tion not merely with trees of their own age, but with older and younger 
trees. The older trees have the advantage of the younger in appropriat- 
ing space vacated by the death of veterans or by the removal of trees 
for any cause. The young trees growing under partial shade are held 
back in height growth, diameter growth and consequent volume growth. 
The economic space occupied by the younger age classes growing under 
partial shade may be defined as the actual percentage of the total grow- 
ing space as represented by the available light, moisture and soil fer- 
tility which is appropriated by these young trees to the exclusion of 
its use by other age classes. This proportion of space so used is exceed- 
ingly small and may be negligible, yet the reproduction may survive 
as scattered individuals for many years. When old trees die, the space 
released is not, as in the case of even-aged stands, occupied entirely 
by reproduction, but is distributed among all of the trees so placed 
that they may avail themselves of it by expanding their crowns. A 
portion only of released space is taken by additional reproduction. 

^ " Concerning Site," Carlos G. Bates, Journal of Forestry, XVI, 1918, p. 383. 
Not only is this basis impractical of measurement and classification in the field, but 
it varies with age of the stand to a much greater degree thkn does mean annual 
growth, hence is not trustworthy as a means of separating sites, though the postulate 
that the best sites are capable of yielding the largest current annual growth is per- 
fectly true. 



THE FORM OF STANDS. EVEN-AGED VERSUS MANY-AGED 389 

The result of these two factors is that the area of an age class is at first 
small, its growth retarded and mortality heavy, but with advancing 
age, the area or per cent of total area occupied by this class increases 
until it reaches a maximum at a period when the stand is at maturity 
and before the loss of veterans begins to leave holes in the canopy. 

TABLE LXI 

Average Crown Spread of Loblolly Pine in the Forest, at Vredenburgh, 

Ala. 



Age. 


Diameter of 
crown. 


Per cent of 
increase in 


Per cent of 
increase in 


Trees per acre 


Years 


Feet 


diameter 


area 




30 


13 








40 


15 5 


19 


42 


140 


50 


19.0 


46 


113 


116 


60 


22.0 


69 


186 


88 


70 


24.5 


88 


255 


70 


80 


27.0 


108 


332 


59 



This law of expansion is illustrated in Fig. 82. 




4 Acres 

I I Area occupied by Crowni 
^^^ Area not occupied by Crowaa 

Even-aged 
stand. 



4 Acrezi 



Single age-class in 
Many-aged forest. 



Fig. 82. — Possible expansion of area occupied by crowns of trees of a given age 
class in a many-aged forest, contrasted with limited expansion possible in 
crown area in an even-aged stand. Loblolly Pine, Ala. Dotted lines show 
possible expansion of 7 per cent in even-aged stand. Shaded area shows pos- 
sible expansion of stand of 332 per cent in many-aged forest. 

On the left, in Fig. 82 an even-aged stand occupies a square area of 4 acres, 417 
feet square. During its growth, crown ex])ansion is effected by a reduction in the 
number of trees from 140 at 40 years, to 59 at 80 years, with much more rapid reduc- 
tion previous to 40 years. The only expansion of area i)ORsib]e for the age class is 
around the edges of the square. The trees can extend their crowns an average of 
14 feet, or 7 feet on one side, in the 50-j'ear period (27-13 feet). This gives a final 
area in square feet of 43P or an expansion of 7 per cent. 



390 FACTORS AFFECTING THE GROWTH OF STANDS 

By increasing the area of the stand, this possible expansion of area becomes less. 
By reducing the area, the per cent of expansion possible becomes greater, since a 
greater per cent of the total number of crowns are so placed as to be able to utilize 
the increased space. The maximum possible expansion occurs when there are but 
59 trees per acre at 30 years, equally spaced, and unobstructed by older age classes, 
in which case the area actually utilized by this age class expands 332 per cent or is 
432 per cent of its original area, and the stand becomes fully stocked at 80 years. 
This expansion of actual are is shown on the right, in Fig. 82. 

This second process is what takes place in a forest composed of stands of many 
different ages. In the case of even-aged stands, thinning or removal of trees simply 
permits the remainder to grow, with no change in area for the class, and the removal 
of the final crop is followed by reproduction which in turn occupies the entire original 
area. But with many-aged stands, when the final crop is removed, which takes place 
on any acre in several different cuttings, the area so released is reproduced only in 
part. The remainder is absorbed by the crown spread of the intermediate age 
classes which thus increase their total area in the manner shown by Fig. 82. 

In the illustration, this stand at 30 years occupies but one-fourth of the total 
area of the 4 acres. The remainder can be occupied by older timber, which in the 
50-year period is removed as it matures. By assuming this 4 acres to be but a part 
of a larger area, and to be distributed over the area coinciding with the distribution 
of the single age class in question, the conditions of a many-aged forest are visualized. 
This factor of crown expansion and competition between different age classes is the 
basis of the diflerences between the increment of many-aged and even-aged stands. 
It explains suppression, economic age, and increased growth after cutting. The 
actual amount of expansion and rate of increase due to this factor will be consider- 
ably less in all instances than the per cents given in table LXI since only a portion 
of the maximum space required by each tree of the class for expansion is available 
at all, and but a part of this can be taken from other age classes. Summed up, 
this factor represents an additional rate of increment to be added to that which an 
even-aged stand of like volume would show, and caused by the fact that the volume 
of the age class in the many-aged forest, while occupying only a certain per cent of 
the area of the forest, is thereby distributed over a much larger area into which its 
crowns can expand. 

299. Annual Increment of Many-aged Stands. The rate of growth 
per year based on a unit of area for many-aged forests does not repre- 
sent production of a single age class, but of the sum of all the age classes 
on the area, averaged for a long period. If desired for a single age 
class, this rate or yield per acre should not be based on the area occupied 
by the timber at maturity divided by the total ages of the trees com- 
posing this stand, for this would greatly under-estimate the rate of 
mean annual growth. The error can be expressed and corrected in 
one of three ways: (1) either the age used as a divisor must be shortened 
to represent the economic age of dominant trees growing in even-aged 
stands, or (2) the area occupied by the mature crop must be reduced 
to represent the average area for the stand during its life, which is 
practically impossible, or (3) to the yield for the period represented 
by the total life of the trees in the stand as actually shown by ring 
counts, must be added the additional yields from other crops of timber 



THE EFFECT OF TREATMENT ON GROWTH 391 

which this same area produced during the period when the final crop 
was only occupying a portion of it. The latter problem may be illus- 
trated best by the yield or rate of growth per year of stands w^hich 
have come up to spruce following poplar or white birch on a burn. 
In the period required to produce a mature crop of spruce, a crop 
of poplar and birch has also been produced. The mean annual growth 
for the whole period must include the total yield of both species. 

Owing to the difficulty of adjusting these yields on one of these 
three bases, it is customary to employ a substitute method of determin- 
ing the rate of growth, not for the total period by any of these adjust- 
ments, but for a partial period, measuring the current periodic growth 
based upon trees or stands which have already reached a given diameter 
or average age. This will be discussed in Chapter XXXI. Its effect 
is to eliminate most of the uncertainty attending the adjustment of 
the factor of competition in many-aged stands, but it introduces the 
question as to whether the current growth measured represents the 
true mean or average for the site over a complete period of crop pro- 
duction. 

300. The Effect of Treatment on Growth. The fact that the growth 
of individual trees demands expansion of their crowns influences 
not merely the yield per acre which may be attained, but more especi- 
ally the dimensions of the individual trees in the stand. Since the 
production of lumber and of certain piece products and the value of 
products grown on a given acre depend much more largely upon dimen- 
sions and sizes and upon quality than upon total cubic volume, yields 
attained in board feet are profoundly influenced by the number of trees 
brought to maturity in stands of equal degrees of crown density or 
stocking. It has been commonly assumed that a normal or fully 
stocked stand simply meant one which showed a complete crown density 
throughout its life regardless or independent of the number of trees 
which composed it. This conception neglects the fundamental idea 
of the tree as an individual. Stands which are fully stocked when 
young, so that crown density is early established, usually become over- 
stocked almost immediately. The normal number of trees, to attain 
best results or highest yields, is least on good sites with strong growing 
species, rapid height growth and correspondingly rapid diameter growth, 
and increases as the sites become poorer. The danger of over-stocking 
and stagnation of both height and diameter growth increases with 
poor sites, even-aged stands, and tendency to abundant reproduction. 
These natural tendencies are affected tremendously by artificial control. 
All operations such as planting, in which the initial spacing is fixed, 
and subsequent thinning by which the resultant number of trees per 
acre at each decade is determined, have a direct effect upon the diam- 



392 FACTORS AFFECTING THE GROWTH OF STANDS 

eter growth of the remaining stand, which in stands continually under 
management may be maintained at an almost constant rate until 
the maturity of the stand. 

It has been found that in stands originally stocked with only part 
of the normal number of trees for smaller ages, as the age of such stands 
advances and the number of trees required in a stand of maximum or 
normal density decreases, the poorly stocked stand tends to approach 
and to equal the yield per acre of the stand which has been normally 
stocked throughout its life. There is therefore a universal tendency 
under natural conditions for stands to approach a full crown cover as 
well as for the more densely stocked stands to become over-stocked. 
This tendency must be recognized in dealing with density factors or 
per cents in prediction of yield and forms a conservative factor in the 
prediction of growth for partly stocked empirical or average stands. 
Ideal conditions for growth are found in stands which have been main- 
tained at a normal number of trees per acre as well as a normal crown 
density through repeated thinnings. Not only is the total volume 
produced per acre and the rate of growth greatly increased by a proper 
balance between thinnings and the remaining stand, but the maturity 
of the stand is hastened and its rotation may be reduced if desired. 

301. Density of Stocking as Affecting Growth and Yields. In 
spite of the tendency of natural stands to approach normal density of 
stocking through the expansion of their crowns, the attainment of 
normality or full stocking under natural conditions of growth is seriously 
interfered with by many agencies. Natural spacing or stocking is 
largely a matter of chance and fails over extensive areas. Much of 
the reproduction may be destroyed during these early years by grazing, 
fires, frost or drought. Saplings and poles may be further destroyed 
by fire, insects and disease. Later on, insects, disease, fire and wind 
continue to make gaps in the age class and crown density. Most of 
these detrimental factors are reduced under protection and the average 
density greatly improved, yet forests covering wide areas ordinarily 
can not be brought to a perfect or full condition of crown cover or stock- 
ing, no matter how intensive the care which is bestowed upon them. 

The yields of forests are desired on the basis of their actual average 
production and not upon the small per cent of stands showing maximum 
or perfect conditions of density and numbers per acre. This gives 
rise to the problem of applying tables of yield to these conditions, first 
as to the selection of areas or plots for the measurement of yields, and 
second, as to whether the area so selected shall be an average of all 
conditions of stocking within the site class or shall make no attempt 
to attain this empirical average. 

It has been generally accepted that the best method of obtaining 



COMPOSITION OF STANDS AS TO SPECIES 393 

yields is to select plots which show a fairly complete crown density, 
not seriously reduced by avoidable factors of damage, and to con- 
struct the table of yields entirely from such plots. This is supposed 
to give the normal relation between yields at different ages for well- 
stocked stands. There remain many variable factors, the chief of 
which is the number of trees per acre in the plots measured. It has 
been suggested that the age or ages at which the final yield is to be 
harvested shall be taken to indicate the normal number of trees per 
acre and that stands of lesser age having this number or more trees, 
while not showing the full yield for these ages may be regarded as fully 
stocked, if not to be cut until the final age. The only difference between 
such stands and stands which remain fully stocked would be found in 
the thinnings in the interval and in the quality and limbiness of the 
timber.^ 

Yield tables based on a given standard such as described may be 
discounted to predict the average degree of stocking for average areas, 
which are known as empirical yields. In some instances efforts have 
been made, by collecting data on large areas, to obtain these empirical 
yields or averages directly in the field instead of by discount from 
yield tables. In either one or the other of these forms, the empirical 
or actual average is the final result desired, and the normal or standard 
yield table is but the means to this end. The arguments in favor of 
obtaining a normal or standard yield table by the selection of plots 
are that the variables represented in the average or empirical stocking 
by differences in form or mixed ages, differences in density and dif- 
ferences in composition of the forest, are eliminated from the table, 
which is confined to showing differences in yield based on site qualities 
and age. The relations of more than two variables can not be accu- 
rately set forth in a single table. 

302. Composition of Stands as to Species. Stands composed of 
a mixture of species may vary in yield from pure stands. Species may 
differ considerably in their capacity for growth and yields even on the 
same site. They vary in height growth and consequently are affected 
differently by the factor of suppression when in mixed stands. The 
rate of survival and the dimensions vary so that the composition of 
the stand changes with its growth. Finally, the original composition, 
independent of these later changes, varies greatly. For these reasons the 
prediction of yields in stands of mixed species has always been regarded 
as extremely difficult. Approximate rather. than accurate results must 
be accepted. Recent investigations indicate that for certain character- 
istic types and mixtures of species naturally growing together, yields 

1 The Use of Yield Tables in Predicting Growth, E. E. Carter, Proc. Soc. Am. 
Foresters, Vol. IX, No. 2, p. 177. 



394 FACTORS AFFECTING THE GROWTH OF STANDS 

determined for the mixed stands do not differ very widely from those 
of pure stands (§ 314). 

References 

Universal Yield Tables, Fricke (Based on height classes); Review Forestry 
Quarterly, Vol. XH, 1914, p. 629. 

Classifying Forest Sites by Height Growth, E. H. Frothingham; Journal of Forestry, 
Vol. XIX, 1921, p. 374. 

A Generalized Yield Table for Even-aged Well-stocked Stands of Southern Upland 
Hardwoods, W. D. Sterrett, Journal of Forestry, Vol. XIX, 1921, p. 382. 

Concerning Site, F. Roth, Forestry Quarterly, Vol. XIV, 1916, p. 3. 

Site Determination and Yield Forecasts in the Southern Appalachians, E. H. Froth- 
ingham, Journal of Forestry, Vol. XIX, 1921, p. 14. 



CHAPTER XXVIII 
NORMAL YIELD TABLES FOR EVEN-AGED STANDS 

303. Definition and Purposes of Yield Tables. A yield table is 
intended to show the yields per acre which can be expected from stands 
of timber at given ages or for given periods, in terms of a given unit 
of volume or of product. 

A complete yield table will show yields for successive decades 
or five-year periods covering the range of age of a species. Ordinarity, 
yield tables do not show the loss in yields per acre during the decadent 
period in over-mature stands, but they can be constructed so as to do 
so. In forests under management, the maximum ages shown are those 
of the oldest stands before cutting. 

Yield tables are used primarily to predict the yield of existing 
stands, hence they are assumed to represent the actual development 
of individual or typical stands throughout their life cycle. This they 
do not always do, since naturally stocked areas tend constantly to pass 
from a condition of under-stocking to one of over-stocking. It follows 
that the most reliable yield tables are those constructed for stands 
grown under management, where thimiings have controlled the incre- 
ment. 

Yield tables are the fundamental data required for the determination 
of the value of forest lands and the profits of forestry, the appraisal 
of damages to forest property, the choice of a rotation or average age 
at which timber should be cut, the advisability of thinnings, the choice 
of species, and the relative profit from expenditures for all forestry 
operations on different sites. An accurate or even an approximate 
knowledge of yields per acre and the average rate of growth per year 
tends to place forestry on a business basis rather than one of blind 
speculation. 

304. Standards for Yield Tables. Yield tables undertake to set 
standards in which the variables affecting yield are eliminated. The 
basis of all yield tables is a separation into site qualities, with separate 
average yields for each quality, since the fundamental variable is site 
quality. 

Form of stand requires separate yield tables for even-aged stands, 
and many-aged stands (§ 252). 

395 



396 NORMAL YIELD TABLES FOR EVEN-AGED STANDS 

The factor of density of stocking (§ 273) separates jaeld tables into 
Normal or Index tables which are based on an average full or maximum 
stocking, and Empirical tables, which represent the actual average 
density of stocking on a given area including partially stocked and 
unstocked portions. 

Composition of the forest is distinguished by constructing tables 
for pure stands (§314) separately from mixed stands. 

The most important distinction is probably that made between 
natural stands and those grown under management. Owing to the 
great influence of treatment upon growth and yields, the standard 
of normahty (see above) is entirely different for natural and for arti- 
ficially grown stands, and yield tables based on the yields of planted, 
thinned and managed forests must be made to replace the present 
normal yield tables, when the material for such measurements becomes 
availalile in sufficient quantity to furnish a proper basis. 

Normal or index yield tables serve their chief purpose as a standard 
of comparison, since most stands will produce either larger or smaller 
yields than those shown (§ 250). This function is better served if 
the standard of normality set by the table is not abnormally high, 
but is made to conform to the results possible of attainment on the 
average acre of the site class, with reasonably thorough protection from 
destructive agencies and reasonal^ly full stocking. 

305. Construction of Yield Tables, Baur's Method. There are two 
methods possible in the preparation of yield tables. The first, known 
as Baur's method ^ is based on the measurement of the present volume 
and age of numerous plots which are then classified as to site and age 
and form the basis of curves of average yields based on age for from 
three to four site classes. This method corresponds with the defini- 
tion of a yield table cited in § 249 since it does not pretend to trace 
the past history of these individual stands; yet the use to which such 
a table is put is to predict from these average curves the growth of a 
given stand by decades. For original stands under natural conditions, 
this method is universally used. The second method is to re-measure 
established plots at stated intervals to determine the volume of growth, 
diminution in number of trees per acre and other changes in the stand. 
While more accurate, the collection of such data must await the growth 
of the timber and the method is best applied to stands under manage- 
ment. 

Yield tables can be constructed by Baur's method on the basis of 
from 50 to 200 plots dependent on the range of site qualities and condi- 
tions of growth. The aim is usually to get at least 100 plots. 

1 Die Holzmesskunde, Franz Baur, Professor of Forestry, University of Munich, 
Bavaria, 1891. 



STANDARD FOR "NORMAL" DENSITY OF STOCKING 397 

306. Standard for '* Normal " Density of Stocking. In selecting 
plots for a yield table, in natural stands, it is neither possible nor advis- 
able to seek areas which show the maximum theoretical density of 
stocking, either as to crown canopy or number of stems per acre. Nor 
should any effort be made to select plots which represent the empirical 
average of stocking. The standard should be to exclude from the plots 
all larger blanks caused by destructive agencies or failure of stocking 
and to select areas reasonably well stocked, with comparatively complete 
crown canopy. This standard of selection should be such that a suf- 
ficient number of plots can be readily obtained from the larger areas, 
without refinements either in size or in location. If too high a standard 
is set, the plots conforming to this standard will be found to be either 
located exclusively on the better portions of each site, or the area of 
the plots' will be too small for safe results. In natural stands this ten- 
dency will lead to the selection of plots containing too great a number 
of trees, which will result later in over-stocking. 

The average yield obtained from plots selected on this basis is 
termed the normal yield, though it may be exceeded by the best plots, 
or by stands grown under management. 

307. Age Classes. The area of a plot should include but one age 
class. Where stands are actually even-aged over considerable areas, 
plots are easily and rapidly located. Where there is difficulty in dis- 
tinguishing the age classes, and in locating areas which exclude all 
trees but those belonging to the class desired, it may be necessary to 
include a few scattered trees of a different age class in order to obtain 
plots of a suitable size. The net area of the plot can then be found 
by deducting the space occupied by these trees, which can be based 
on the area covered by their crown spread, modified in open stands 
to include a proper proportion of the gaps in the crown cover. 

Stands whose period of reproduction is from ten to thirty years, 
depending on site and climatic factors, but which may still be classed 
as even-aged stands (§ 259) will be measured as such and their average 
age determined. 

308. Area of Plots. The value of a single plot in indicating normal 
yield increases with its size, within the limit which permits of securing 
a uniform stocking and crown cov^r conforming with the standard 
sought. Since one plot represents but a single age and one shade of 
site quality, and the cost of measurement increases with size, it is better 
to limit the size of plots for a yield table and obtain a greater number 
more widely distributed. 

The size of plots should increase with the size and age of the trees 
to be measured. The greatest danger in measuring small plots is 
failure to coordinate the quantitative site factors utilized in producing 



398 



NORMAL YIELD TABLES FOR EVEN-AGED STANDS 




the yield with the area measured. This error is best illustrated by the 
measurement of an isolated clump of trees with wide crown and root 
spread. A plot laid out to include their boles will have too small 
an area, and an excessive yield (Fig. 83). 

In dry regions especially, root spread exceeds that of crowns and 
cannot be determined accurately. The effect of these errors is especially 
noticeable when the size of the plots is small, the yield per acre varying 
inversely with area of plots. By increasing the size of the plot, the 
proportional influence of a faulty location of its boundaries is lessened, 
and when coupled with care in making these boundaries inclusive of 
crown space and probable root space of the trees measured, the error 
is negligible. Just as for other sample plots (§ 243), it is better to 
have a smaller plot surrounded by a control strip of similar timber than 

to extend the 
boundaries to in- 
clude the whole 
of a stand to be 
measured, and it 
is usually possi- 
ble, in regions of 
average rainfall, 
to have such a 
control strip. 
The size of plots 
under the above 
principles will 
vary from ys- 
acre, for dense 
young stands, to 5 acres for veteran scattered timber in dry regions. 
Ordinary sizes run from j to 2 acres. Since these boundaries 
should be accurately run, plots should be square or rectangular, 
and since the area contributing to the growth of single trees is 
in theory a circle, rectangular plots should not be too narrow: their 
short dimension should be at least four times the average width of 
cro\»^ns of the trees measured. For the same reason plots should never 
be triangular or have sharp angles. Unless intended for permanent 
location and re-measurement, the corners of plots are marked tempora- 
rily by any convenient means, and their side lines blazed or marked 
so as to exclude all trees falling outside of the boundary. 

309. Measurements Required on Each Plot. Dimensions of Trees. 
A diameter limit is determined, dependent on minimum merchantable 
sizes. All trees above this are measured at B.H. and recorded in diam- 
eter classes of 1 inch or 2 inches. Since these plots are for the purpose 



Fig. 83. — Relation between growing space occupied by crowns 
or roots of trees and size of plot measured to secure 
yield per acre. 

A — Too small an area. 

B — Correct for humid region or site. 

C — Approximately correct for arid region. 



MEASUREMENTS REQUIRED ON EACH PLOT 399 

of measuring yields they are selected in stands which have reached 
merchantable sizes. Plots on which a portion only of the trees are 
merchantable may require the counting of the remaining stand and its 
classification as to size. Dead trees are recorded by diameter. Species 
are separately tallied. 

The height of trees for a yield table should be taken separately 
on each plot. Several tn^es of different diameters, whose heights are 
average for the stand should be measured and recorded together with 
their diameters, the number varying with the stand, from 5 to 15. 
Where merchantable and not total height is desired, the satisfactory 
determination of heights for the plot is made much more difficult by 
the variation in top diameters and the danger of error in judging heights. 
Such a yield table, while practical, is less reliable than one based on 
total heights. Total height should always be recorded regardless of 
whether merchantable height is used, since it is required for a permanent 
standard of site quality. 

Where the merchantable height unit is used it may be better to tally 
the merchantable length of every tree on the plot than to rely on a few 
trees measured by the hypsometer. This introduces the element of 
ocular guess. 

Age and Volume of Stand. The age of each plot is separately 
determined by methods discussed in Chapter XXIII. The common 
method of determining the volume on the plot is by standard volume 
tables, based on diameter and height. This assumes that the variation 
of the trees on each plot as to shape or form quotients from the average 
form for this species or region, is not sufficient to require separate 
determination. Since trees must either be felled or cut into, to deter- 
mine age, except when the increment borer will suffice, and since the 
trees selected for this purpose would be average in volume for the stand 
or for diameter groups within it, these sample trees are sometimes used 
to determine the volume of the stand. This method is useful when no 
reliable volume table exists, and when cubic volume is sought. The 
additional accuracy attained in measuring the volume of the sample 
trees for the plot itself is offset by the possibility that the trees cut 
may vary from the true average of the stand. The methods of deter- 
mining the size of such sample trees for felling are described in § 241. 

Crown Classes. Each tree on the plot is usually tallied in the crown 
class in which it falls, as classified in § 274. 

Description of Plot or Site. Since in the preparation of a yield no 
effort is made to classify the plots into site qualities by inspection of 
the site factors in the field, the description of the plot should be brief, 
and serve merely to explain the results obtained and check their value.. 
The points to be covered are the following: 



400 NORMAL YIELD TABLES FOR EVEN-AGED STANDS 

1. Location of plot. Region, watershed or block, section or forty. 
Relocation is not contemplated from this description. 

2. Density of crown cover. This has in some studies been used 
in an attempt to reduce the area to a fixed standard of density; e.g., 
a stand showing .9 crown density would be considered as the equivalent 
of but .9 of a full yield on the plot. The element of judgment thus 
introduced is dangerous and had best be omitted. 

3. Altitude: 

Absolute — approximate. 

Relative — with respect to nearest stream, when it affects the 
quality of site. 

4. Aspect — as affecting exposure. 

5. Degree of slope. 

6. Geological formation. 

7. Soil, kind, depth, consistency and degree of moisture. 

8. Origin of stand, whether from sprouts or from seed. 

9. History of stand. 

10. Condition of stand with respect to evidence of damage caused 
by fire, insects, wind or other agencies should be especially noted. 

11. Exposure to winds, degree and character. 

12. Amount and character of tree reproduction on the ground. 

13. Herbaceous and shrubby vegetation under the timber. 

Record of Data for each plot. The data of permanent value for each 
plot are, 

1. Area, in acres. 

2. Age. 

3. Total number of living trees, by species. 

4. Number of living trees above merchantable diameter limit, by 

species. (This may be shown for two diameter limits, as for 
cordwood and saw timber units.) 

5. Average diameter (from diameter of tree of average basal area, 

or volume) (§ 242). 

6. Height of dominant trees, or dominant height of stand; total; 

merchantable. 

7. Total basal area at B. H. of trees per acre, in square feet. 

This is a valuable index to density of stocking. 

8. Yield per acre, in cubic feet, total. 

9. Yield per acre, in merchantable units, to given top diameters 

and stump heights. 
10. Dead standing trees, number or per cent. 
■ 11. Density of crown cover. 
12. Description of plot. 



TABLE WITH SITE CLASSES BASED ON HEIGHT GROWTH 401 

310. Construction of Yield Table with Site Classes Based on Height 
Growth. There are two possible bases on which to sepai'ate site quality, 
namely yields or rate of growth, and total height or height growth. 
In choosing between these as the basis of site quality, not only must 
the construction of the table be considered but also its later application 
in the field. Whichever basis is used, the range of growth for a species 
or region must be divided arbitrarily into site classes, once its maximum 
and minimum limits are determined. When volume or yield is chosen 
as the direct basis of site classes, regular and consistent results may be 
obtained by eliminating most of the variables in the choice of plots. 
But when these results arc later used as a means of determining site 
qualities in the field on the basis of mean annual rate of growth per year 
or total yield based on age, the system breaks down. 

On the other hand, if the division of plots into site qualities is based 
on height growth as indicated in § 296 not only are the original plots 
apt to be separated more accurately into their true site classes since 
variations in volume due to over- or under-stocking as reflected in the 
board foot or other unit are minimized, but the division of a large 
area in the field into site classes for the application of the growth data 
in predicting yields is made possible in strict conformity with the 
standard used in the table itself (§ 345). 

While volume has been made the direct basis of many European 
yield tables, yet in these regulated and fully stocked stands most of 
the variables are reduced to reasonable proportions. Under our con- 
ditions of abnormal and accidental stocking, with the maximum of 
damage to the stands during growth, the variations from the factor 
of density of stocking due to variable number of trees per acre, even 
in stands of full crown cover, is so great as to discourage most investi- 
gators on first attempt. 

The steps in the construction of a yield table based on height are 
as follows: 

1. On cross-section paper on which age is plotted on the horizontal 
scale, and height on the vertical scale, place the average height for each 
plot above the age of the stand. These heights may be the heights of 
the dominant trees (§ 296). These points will fall in a comet-shaped 
band increasing with age. 

2. Draw a curve indicating the maximum height growth, and one 
for minimum height growth as in Fig. 84. 

3. Decide upon the number of site classes to use. These will depend 
largely on the total range of heights found for trees of a given age, and 
the possibility of convenient subdivisions not too small to be serviceable, 
i.e., large enough to overcome the slight variations in height based on 
age which may be due to density of stand instead of site. 



402 



NORMAL YIELD TABLES FOR EVEN-AGED STANDS 



4. Divide the space between the maximum and minimum curves, on 
each ordinate, into arbitrary spaces of equal magnitude, corresponding 
to the number of site classes established, and connect the points so found 
by curves. 

5. The numbered plots whose height falls in each division of the 
chart are assigned to the indicated site quality. Owing to variables 
affecting yield, some of the plots in a lower site class may exceed the 
growth of plots whose site class is better. 



90 



75 



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80 


























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70 




















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10 



20 



40 50 
Age, years 



60 



70 



80 



90 



Fig. 84. — Method of separating plots into three site quaUties based on the height 
attained by dominant trees in the stand, plotted on age of stand. Jack Pine, 
Minnesota. 



The height of dominant trees on 131 plots of jack pine, plotted on 
the basis of age, is shown in Fig. 84. By this method (Baur's), the 
positions of the maximum and minimum curves determine that of the 
curves separating the site qualities. One or two plots with abnormally 
rapid or slow growth must not be permitted to influence unduly the 
position of these outer curves. With height, the true position of the 
boundary curves can be found with greater certainty than if volume is 
used originally as the basis of classification. In this figure, the average 
heights of qualities I, II and III at 100 years were taken as 90, 75 and 



TABLE WITH SITE CLASSES BASED ON HEIGHT GROWTH 403 

60 feet, following the suggestion of Roth as an example of class C in 
height classification (Table LV, § 296), and with these guiding 
points the curves limiting the three classes were drawn by Baur's 
method. 

6. The yield of all plots in a single site class are then plotted on 
cross-section paper whose base or horizontal scale is age, and whose 
vertical scale is volume. From these data, a curve of average yield 




100 no 120 130 1.40 
Age. Years 



160 170 180 ISO 



Fig. 85. — Curves of yield obtained by averaging the yields of plots whose height 
growth has placed them in the same site class. The final curves smooth off 
irregularities in these averages. Second growth Western Yellow Pine, California. 
S. B. Show. 



based on age may be drawn from which the 3delds for the site class 
for each decade or five-year period are read. A separate curve is plotted 
for each site class. The yield table finally shows the average yields 
based on age for each separate site class. 



404 NORMAL YIELD TABLES FOR EVEN-AGED STANDS 

When constructed on this basis, yields for different site classes 
increase at a greater ratio than do the indicating heights. 

In drawing the curve of yield based on age for a single site class, 
it is best to first obtain the average yield for a given decade by arith- 
metical means and connect these averages by straight lines. Even if 
each plot were normal, the averages at different points might fall above 
or below the mean for the site as the plots happened to be on the better 
or poorer portions of this site class — and to this factor, the natural vari- 
ation in density or yield is added. 

7. For this reason, the average curves so constructed, for each 
site class, should now be assembled on a single sheet, as shown in Fig. 
85. The curves of yield based on age can then be harmonized for all 
site classes by the same principle as used for volume tables (§ 140).^ 

311. Rejection of Abnormal Plots. As shown in § 304, the intent 
of this table is to establish a standard of yield, termed normal or index, 
with which the yields of any existing stand may be compared. After 
the separation based on height growth is effected, the yields of plots 
in the same site class will show great variation, due to the 

Natural range of site quality within the arbitrary boundaries 

established; 
Numl)er of trees per acre in the natural stocking; 
Completeness of the crown canopy. 

The eccentric behavior of the averages plotted in Fig. 85 indicates the 
effect of these variations in yield. The question arises as to whether 
all of the plots should be included in these averages or certain plots 
rejected as abnormally stocked. A method of correcting the yields 
by a factor of density of crown has been generally rejected as unsatis- 
factory (§ 309). The area of plots is accepted as measured. There 
are, then, two possibilities of rejection; first, by ocular selection in the 
field, which eliminates those plots which are incompletely stocked; 
second, by further inspection of the plotted volumes based on age. 

Baur's rule for rejection of plots is quoted by Graves as follows: 
"Stands which have the same age and average height are compared, 
and all are considered normal whose basal area lies within a range of 
15 per cent; that is, the basal area of the best and poorest stocked stands 
must not differ more than 15 per cent." ^ The application of this rule 
rests upon the interpretation of the term " average height." Where 
from three to five site classes are made as in Fig. 85, and a curve of 
average height is found for each site class, which would fall midway of 

^The yields shown in Fig. 85 are from an unpublished manuscript by S. B. 
Show, U. S. Forest Service, California, for second growth Western yellow pine. 
" Graves' Forest Mensuration, p. 319. 



REJECTION OF ABNORMAL PLOTS 405 

the limits shown in the figure, the rule has been applied in this country 
to all plots whose heights classify them with a given site. The natural 
variation in volume for plots within one site class is greater than 15 per 
cent, independent of abnormalities — hence if all plots which vary 7| 
per cent above or below the average volume for the site at that age are 
rejected, about half of the plots, although noYmal, may be thrown out. 
If this rule is to be correctly applied as a test of normality, the arbitrary 
permitted variation of 15 per cent, if used at all, should first be corrected 
by finding what the normal yield of the particular plot should be, based 
on its actual height. If height for the plot is midway between quality 
I and II, normal yield is also midway between the averages for these 
qualities. The steps necessary would be as follows: 

1. Draw curves of average height as shown in Fig. 84, and curves 
of average volume as shown in Fig. 85. 

2. Determine the per cent of variation above or below average height, 
for each plot, and subtract or add the same per cent from the volume of 
the plot. This gives the corrected volume of the plot based on 
average height for the site. 

3. Compare the corrected volume of the plot with the average volume 
for the site. If it falls above or below the calculated normal by more 
than the desired per cent of error the plot can be thrown out. 

4. After testing the normality of all plots, re-compute the average, 
using only those plots accepted as conforming to the standard. 

If 15 per cent is a proper standard of variation for forests under 
management, it is probable that even with the above method this per 
cent is too small as a criterion of normality for natural stands. It 
should be possible, by eye, to select plots of which at least 95 per cent 
will be suitable for inclusion in obtaining the average results for a stand- 
ard yield table. With a range of basal area increased to 25 per cent 
for plots of the same height based on age as indicated, it is probable that 
only distinctly abnormal plots will be rejected. 

In constructing volume tables it is not customary to reject trees 
after they have been measured for volume, since rejection can take 
place in the selection of the tree. With plots for yield tables, the desire 
to secure a theoretically normal or uniform standard may easily lead 
to too rigid a rejection of plots which are entirely suitable for the aver- 
age sought. Maximum yields, on the basis of site alone, should never 
be sought by these average curves of yield, since the best portions of 
the site will exceed the average. Again, such tables, if made for natural 
stands, should show what can reasonably be expected in stands repro- 
duced naturally and not thinned, on the average acre for site. A con- 
sistent average showing the probable progress of a fully or normally 
stocked acre by decades, and not an abnormal maximum yield, is the 



406 NORMAL YIELD TABLES FOR EVEN-AGED STANDS 

object sought both in field selection of plots and in their further sifting 
in the office for the preparation of normal yield tables for natural 
growth. 

312. Construction of Yield Table with Site Classes Based Directly 
on Yields per Acre. The main objection to the direct classification 
of site on the basis of yield or volume on age by Baur's method is the 
impossibility of using this basis later as a means of classifying forest 
lands into site qualities from field examination. Furthermore, yield 
alone gives an unsatisfactory basis for correlating yield tables for given 
species when made for different regions, or for correlating the yields 
of different though similar species. It is this need of standardization 
that has led to the adoption of height growth rather than volume as 
the basic standard. 

A further objection to the direct use of yields lies in the method of 
plotting, and the testing of plots for normal density. By this method, 
the volumes of all plots, based on age, are entered on the same sheet as 
shown in Fig. 86. The drawing of the maximum and minimum curves 
is the next step. There is no way by which the abnormality of the plots 
can be first tested as with heights. So the elimination consists wholly 
of drawing these boundary lines to exclude certain plots whose yield 
is so much greater or smaller than the remainder that their inclusion 
would unduly influence the position of these limiting curves. 

The third step is to divide the space thus blocked off into equal 
bands by the method used for height, i.e., by dividing the distance 
on each ortlinate into equal parts, and connecting the points so estab- 
lished. 

Finally, a curve is drawn exactly midway of each space as described 
for height (§ 310), and the values are read from this curve at each decade 
to form the table of yield based on age. 

By this method yields increase with site quality by exact intervals. 
No averages are attempted,, and the result is entirely independent of 
height and is influenced principally by the maximum and minimum 
yields rather than the general weight of the plots studied. 

Using as the basis the plots which have been classed as belonging 
to each separate site by either of the above methods, curves showing 
the average at different ages can also be prepared for the following 
additional data: 

Number of trees per acre; 

Total, 

Above a minimum diameter. 
Average diameter. 
Average height of dominant trees. 
Total basal area. 



YIELD TABLES FOR STANDS GROWN UNDER MANAGEMENT 407 



313. Yield Tables for Stands Grown under Management. Normal 
yield tables for stands grown under management may be constructed 
by the above methods, whenever plots are available which have been 
under proper management, but may in the course of time be checked 
and finally supplemented entirely if desirable by the yields of plots 
which have been measured at intervals of from five to ten vears. 



4000 



3500 



3000 



2500 



2000 



1500 



1000 



500 



























-^ 


























y 


/f 




^^- 


^--" 


I 


















• 


/ m 


/" 


.-^^ 


• 


• 






















••/ 








• 


^ 






















/ 


» / 
/ 

/ 




y 


• 


• 


•^.- 


• 

II 


















/ • 


/ 


» 


» • 




^^ 




» 
1 


. 














/ / 
/• / 


\'y 


/• 


• 




• 


^^ 


• 
















• 




*/' 


. / 




• ^^ 


\^ 




























^^ 








III 
















i / 
1 /• 




» 


/ 


• 


.*^-- 


.--' 


' 
















1 1 
1 1 
1 1 
1 1 


/ / 




Y 


,^'' 


y'^ • 


' 


* 


















1 1 1 
1 1 
1 I 




• • 


• 


/ 


y 


y^ 


















/ / 


' 1 
/ ,'■ 


I / 






/ 


y 


















/ 


/ / 


/ J 
/ / 

1 / 




y 


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y^ 


/- 


























■'^-^' 



























































10 



20 



30 



40 
Age, Years 



50 



60 



70 



80 



Fig. 86. — Curves of yield based directly on cubic volume plotted on age. Jack 

Pine, Minne.sota. 

WTiere a series of plots, differing in age by ten years, is available, 
the measurement a decade later on these plots will give fragments of 
a curve of growth which may be pieced together. The greater the 
period over which these re-measurements extend, the more nearly do 
these fragmentary curves form a complete series. 

It may be expected that yields on areas under treatment will exceed 
the so-called normal yields used as a standard for natural growth. 



408 NORMAL YIELD TABLES FOR EVEN-AGED STANDS 

The latter tables thus become the basis or minimum from which such 
increased yields may be computetl for fully stocked areas. 

314. Yield Tables for Stands of Mixed Species. Practically all 
stands are composed of more than one species, though some conifers 
as Western yellow pine and lodgepole pine grow in practically pure 
stands. So prevalent is the mixture that a stand which is composed 
of 80 per cent and over in volume for the given age class of a single 
species is termed a pure stand of that species. There may exist a large 
number of trees in an under-story of different species, and yet the volume 
of the trees of other species in the main stand may not exceed 20 per 
cent. 

In even-aged stands composed of two or more species in mixture, 
two methods have been proposed for the determination of yields. One 
is to prepare yield tables for pure stands of each species, and then to 
determine the per cent of these species in the mixed stand. The further 
yield of such a stand is predicted by applying the per cent thus indicated, 
to each yield table, and taking the sum of the two partial yields as the 
yield of the mixed stand. 

In applying these tables on this basis to get yields for the future 
from young stands, the question of survival may affect the result, in 
case one species tends to crowd out another. But when stands are 
even-aged, the association is apt to be of species which customarily 
grow in mixture and maintain their places in the stand. The yields, 
however, will be for the per cent of future, not of present mixture. 

Where species differ radically in their characters, and grow in a 
mixed stand, such as a hardwood species with conifers, there is apt to 
be greater variation in yields, but with trees of similar habits, such 
as mixed sprout hardwoods or mixtures of two or more conifers, the 
stand behaves much as it would for pure stands. 

For all such even-aged mixed stands, it is possible to prepare yield 
tables by disregarding the per cent of mixture, or recording it merely 
as a descriptive item, and proceeding as if the stand were pure. 

An example ^ of a yield table for mixed stands of second-growth hardwoods in 
New England is given below. The conclusions based on this study were, first, that 
in spite of wide variation in percentages of species in mixture, for a given age, site, 
and density, the volumes in board feet, cubic feet and cords were constant, and, 
second, that the volumes of trees of given height and diameter in cords and cubic 
feet were the same, regardless of species. 

1 Bulletin of the Harvard Forest No. 1. Growth Study and Normal Yield Tables 
for Second-Growth Hardwood Stands in Central New England. By J. Nelson 
Spaeth, Cambridge, Mass., 1921. 



YIELD TABLES FOR STANDS OF MIXED SPECIES 



409 



TABLE LXII 

Normal Yield per Acre in Cubic Feet and Cords of Better Second-growth 
Hardwood Stands in Central New England 

site class i 
(All trees 2 inches in diameter and over) 



Age 


Trees 


Basal 


Height 


DB.H. 


Volume 


Vclume 


Forest 


in 


per 


area 


in 


in 


per acre. 


per acre. 


form 


Years 


acre 


Sq. ft. 


Feet 


Inches 


Cu. ft. 


Cords 


factor 


20 


1250 


66.0 


27.1 


3.11 


1041 


15.80 


0.582 


25 


1120 


90.8 


33.0 


3.86 


1625 


23.71 


.542 


30 


1010 


107.2 


37.5 


4.41 


2150 


29.75 


.501 


35 


900 


119.9 


41.5 


4.94 


2628 


34.96 


.503 


40 


800 


130.2 


45.0 


5.46 


3058 


39.63 


.520 


45 


700 


139.7 


48.2 


6.05 


3495 


44.03 


.520 


50 


610 


148.0 


50.7 


6.69 


3898 


48.00 


.520 


55 


525 


155.7 


53.1 


7.37 


4298 


51.84 


.520 


60 


450 


162.5 


55.4 


8.14 


4677 


55.50 


.520 


65 


390 


169.0 


57.8 


8.91 


5068 


59 . 25 


.520 


70 


340 


175 1 


59.8 


9.72 


5462 


62 . 75 


.522 


75 


300 


180.9 


61.9 


10.51 


5833 


66.18 


.521 


80 


270 


186.3 


64.0 


11.25 


6200 


69.50 


.520 



SITE CLASS II 

(All trees 2 inches in diameter and over) 



Age 


Trees 


Basal 


Height 


DB.H. 


Volume 


Volume 


Forest 


in 


per 


area. 


in 


Ill 


per acre. 


per acre. 


form 


Years 


acre 


Sq. ft. 


Feet 


Inches 


Cu. ft. 


■ Cords 


factor 


25 


1360 


59.8 


27.8 


2.84 


982 


14.65 


0.593 


30 


1235 


77.9 


31.8 


3.40 


1380 


20.40 


.557 


35 


1125 


91.1 


34.8 


3.86 


1798 


25.48 


.567 


40 


1030 


101.6 


37.4 


4.25 


2180 


29.53 


.574 


45 


940 


110 3 


39.8 


4.66 


2534 


33.04 


.577 


50 


855 


117.9 


41.5 


4.94 


2828 


35.98 


.580 


55 


775 


124.6 


42.8 


5.43 


3118 


38.55 


.584 


60 


700 


130.7 


44.2 


5.85 


3375 


41.08 


.584 


65 


630 


136.6 


45.3 


6.31 


3638 


43.42 


.587 


70 


565 


142.2 


46.3 


6.79 


3895 


45.61 


.592 


75 


500 


147.7 


47.0 


7.36 


4146 


47.75 


.598 


80 


440 


153.0 


47.6 


7.78 


4390 


49.80 


.601 



The percentage of species in mixture in the stands comprising the above tables ia 
shown in Table LXIII. 



410 



NORMAL YIELD TABLES FOR EVEN-AGED STANDS 



TABLE LXIII 

Percentage of the Various Species in Mixture from Table LXII Classified 

AS TO Type and Site Class 





Oak, 
Red 


Maple 


Birch 


Beech 


Ch't- 
nut 


Bass- 
wood 


Pop- 
lar 


Ash, 
white 




Better Hwd 


Red 


Hard 


Gray 


Paper 


Yel. 


Misc.* 


Qual. I 
Qual. II 
Inf. Hwd. 


27 
20 

2 


15 
12 
24 


3 
6 
2 






38 


2 
8 
3 


8 
10 

4 


2 

7 



6 
5 
1 


.9 
3 



7 

8 

15 


15 
14 

1 


6 

7 

10 



* Under miscellaneous are included all species whose combined representation in the plots of 
any one type or site class is less than 5 per cent of the total number of trees. These species 
are: white oak, black cherry, pignut hickory, white pine, hemlock, elm, butternut, hop horn- 
beam, black birch, flowering dogwood, and shad bush. 

By either of the above two methods of constructing yield tables for 
mixed stands, the yield of the entire stand is taken as the standard of 
yields.! 

The classification of mixed stand may be greatly simplified by group- 
ing together all plots in which 80 per cent or over of the merchantable 
volume is made up of certain species. In a study of the mixed conifer 
type on the Plumas National Forest in California, containing Western 
yellow pine, sugar pine, Douglas fir, white fir, and incense cedar, 
75 per cent of 156 plots were found to contain but two principal species 
whose combined volume was over 80 per cent of the plot. The yields 
could l)e grouped as 

1. Yellow pine — Douglas fir. 

2. Yellow pine — Fir (Douglas or white). 

3. Douglas fir — white fir. 

As indicating the possibilities of simplifying the problem of yields of 
mixed stands, it was found in this study that the average basal areas, for 
plots showing the same standard of height growth (§ 296) was as follows: 



Type 


Basic plots 


Per cents of yellow 

pine — Douglas fir 

type 


Yellow pine — Douglas fir 


43 
65 
21 


100.0 


Douglas fir — white fir . 


97 


Yellow pine — fir 


105.1 







^ A method by which the per cent of yields in plots of mixed species is recorded 
on the cross section paper, and the yield per acre expressed for different species 
which constitute different per cents of the total stand, is described in Graves' 
Forest Mensuration, Chapter XVII, p. 332. 



REFERENCES 411 

This result strengths the conclusion that for species which form 
part of the same crown canopy, differences in total yield, of plots with 
different per cents of mixture, may not constitute a serious obstacle 
to the construction of yield tables based on age.^ 

References 

Rate of Growth of Conifers in the British Isles. Bui. 3, Forestry Commission, 
1920. 

Comparison of Yields in the White Mountains and Southern Appalachians, K. W. 
Woodward, Forestry Quarterly, Vol. XI, 1913, p. 503. 

Einheitliche Schatzungstafel fur Kiefer, Zeitschrift fiir Forest- und Jagdwesen, June, 
1914, p. 325. Review, Forestry Quarterly, Vol. XII, 1914, p. 629. 

The Use of Yield Tables in Predicting Growth, E. E. Carter, Proc. Soc. Am. Foresters, 
Vol. IX, 1914, p. 177. 

Yields of Mixed Stands, Schwappach, Untersuchungen in Mischbestanden, Zeit- 
schrift fiir Forest- und Jagdwesen, Aug., 1914, p. 472. Review, Forestry 
Quarterly, Vol. XIII, 1915, p. 98. 

1 A Preliminary Study of Growth and Yield of Mixed Stands, S. B. Show and 
Duncan Dunning, U. S. Forest Service, San Francisco, Cal., 1921. Unpublished 
manuscript. 



CHAPTER XXIX 

THE USE OF YIELD TABLES IN THE PREDICTION OF GROWTH 
IN EVEN-AGED STANDS, WITH APPLICATION TO LARGE 
AGE GROUPS 

315. Factors Affecting the Probable Accuracy of Yield Predictions. 

If the average yield on Quality I site for a species is taken as 100 per 
cent, and but three qualities are distinguished, the relative yields shown 
for Qualities II and III may be as low as 72 and 45 per cent of that on 
Quality I, respectively.^ This means gaps of 28 and 27 per cent in the 
series between the points arbitrarily marked by the average curves 
expressed in the yield table. The use of five qualities of site reduce 
these intervals to about 15 per cent. For young stands, or areas just 
growing up to timber, this is as close a prediction as can be expected. 
If the site is properly classified, its future yield if normally stocked will 
differ by an extreme of one-half of the above interval, either above 
or below the standard. Once the site is identified bj^ the use of average 
height based on age, the future yields can be predicted by use of the 
yield table, either for bare land or for partly grown young stands, 
provided the degree of stocking agrees with that incorporated in the 
table. 

The larger part of the area of any natural forest is not comparable 
with these conditions. The variables of density of stocking, form of 
age classes, and composition of species must all be dealt with before 
yields on any considerable area can be predicted within the desired mar- 
gin of accuracy. The degree of accuracy attainable in prediction of 
yields in our wild forests is not yet known even approximately since 
for many-aged forests and mixed stands, yield tables based on age 
have not been attempted untU recently (§ 314). This much can be 
said — the degree of accuracy attainable, and hence required, is greatest 
for short periods, i.e., for the current growth of a decade or two, and 
diminishes as the length of the period increases. But the relative 
importance of accuracy also diminishes with the length of the period, 
thus permitting the use of yield tables based on averages. 

1 Norway Pine in the Lake States, U. S. Dept. Agr., 1914, Bui. 139, p. 15. ' 

412 



ACTUAL OR EMPIRICAL DENSITY OF STOCKING 413 

316. Methods of Determining Actual or Empirical Density of 
Stocking. For even-aged, pure stands, but one variable is present 
in addition to site quality, that of the density of stocking. As this 
variable is the result, first, of the intrusion of small areas of unstocked 
land into the timbered area, which it may not pay to exclude in mapping 
(§ 306) and second, of the uninterrupted play of natural agencies of 
destruction operating on stands which are themselves originally the 
result of chance at the time of reproduction, the problem is to arrive 
at an average yield per acre which expresses not so much the capacity 
of the site as the accidental product of these various conditions. This 
average will in all cases be less than the standard or normal yields for 
the same area, sometimes by as much as 50 per cent. Evidently the 
determination of site quality is but the first step in predicting the yields 
of existing stands from such a standard table, and without correction 
these predictions may range from 50 to 100 per cent too high except 
on small tracts, such as plantations or managed forests, whose density 
factor is known to coincide closely with the yield table. 

Use of Empirical Yield Tables. There are two methods of over- 
coming this difficulty. The first is an attempt to arrive directly at 
the average yields based on age for the larger area, or to make an empir- 
ical yield table (§ 303) which will reflect the degree of stocking present. 
This applies the principle used in timber estimating in determining the 
volume of the average acre (§ 209). But the operation is more dif- 
ficult, as it involves the separation of the entire area into stands based 
on age, whose area is known, and the combining of these data into a 
yield table subnormal in character and representing a purely arbitrary 
percentage of standard yields. In the preparation of such a table, the 
curves of yield are affected by the varying per cents of stocking of dif- 
ferent age classes and areas so that practically the entire area must be 
analyzed to obtain the true average, and then the table will be incorrect 
in its prediction of yield for any specific age class or stand which differs 
from this arbitrary average stocking. The table will be correct only 
for the tract on which it is made since empirical density varies with 
every forest and block. Empirical yield tables on this basis have the 
same drawbacks as volume tables for defective trees which express 
the net contents only (§ 151). 

Use of Normal Yield Tables by Reduction. The better plan, and 
the one which will probably be universally used, is to depend upon a 
standard normal yield table (just as -upon a volume table for sound 
trees only) and to ascertain the relation or percentage of deduction from 
this table, which applies to the specific stand or larger area for which 
yield is desired. For even-aged stands, the application of the yield 



414 THE USE OF YIELD TABLES 

table to the larger area involves the same steps for this area as are 
required in the construction of the normal yield table itself, or for the 
preparation of an average empirical yield table. These are as 
follows: 

1. Determine the volume, the area occupied, and the age of each 
separate age class. 

2. From these data in turn compute the volume per acre for the given 
age. 

3. Determine the relative density by dividing this unit volume by 
the yield of an acre of the same age from the yield table; this is expressed 
as a per cent of the standard yield for that age. Per cent density can 
thus be found separately for each age class, or for each separate stand 
if desired. 

317. Application of Density Factor in Prediction of Growth from 
Yield Tables. Future yield can now be predicted for all stands from 
the same yield table,- by applying the reduction per cent to this table 
which is required by the stand or age class in question. 

Influence of Number of Trees per Acr^. There is one valid objec- 
tion to this assumption that relative density as expressed at a given 
age in terms of volume will remain constant for future yields and that 
is that under the laws of growth of stands partially stocked this stand 
will tend to become fully stocked (§301). A knowledge of the number 
of trees per acre required for full stocking at the age of cutting is also 
obtained from a normal yield table, and this knowledge may be directly 
applied in determining the per cent of density in immature stands, 
not on the basis of crown cover existent but of the ultimate yield to 
be expected from the trees which will probably survive. In the same 
way, for older stands, when volume per acre is less than that in a nor- 
mal stand, but the number of trees per acre is sufficient, the reduction 
can be lessened as applied to these partially stocked stands as long as 
the trees are so distributed as to utilize the area; e.g., in one case, 
a 50 per cent average stocking may represent 100 per cent stocking on 
50 per cent of the area, with the rest blank. No correction should 
be made. In another case the entire area is covered with a stand whose 
volume is 50 per cent of normal, but trees are well placed. In this case 
the yield will probably be normal at the age at which the normal num- 
ber of trees per acre drops to about the average number now present in 
the natural stand. 

The former or simpler method is of course extremely conservative 
and allows a margin for the continuance of natural losses by fire, wind, 
insects and diseases, while the latter may be applied to more intensively 
managed and better protected forests. 



PREDICTION OF GROWTH FROM YIELD TABLES 



415 



This method is illustrated below based on a standard yield table, § 314. 
Second-growth Habdwoods in Central New England 
Site Class I 















Prediction of 








Actual 


Standard 




Yield 63 Per Cent 


Area. 


Age. 


Yield. 


Yield, 
per 


Yield 
per 


Reduction. 


OF Standard in 








acre. 


acre. 




10 Years. 


20 Years. 


Acres 


Years 


Cords 


Cords 


Cords 


Per cent 


Cords 


Cords 


10 


25 


150 


15 


23.71 


63 


22 


27.7 



This assumes no increase in the density factor with age and is the most conserva- 
tive method. 

Assuming that future yield will be influenced by the number of trees and their 
distribution, the future yields as shown may be increased as follows: 



Number of 

trees 
per acre now 


Normal 

number in 

10 years 


Reduction 

per cent in 

10 years 


Yield in 

10 years. 

Cords 


Normal 

number in 

20 years 


Reduction 

per cent in 

20 years 


Yield in 

20 years. 

Cords 


600 


900 


66 1 


23.3 


700 


86 


37.8 



This basis gives the maximum possible yields to be expected by contrast to the 
first method, since it does not contemplate the loss of any of the original six hundred 
trees, and assumes that these trees are distributed at equally spaced intervals over 
the area. 

Somewhere between these two predictions the actual future yield will be found. 

Use of Basal Areas. Basal area may be substituted for yields in 
determining the percentage relations, and as a basis for predicting 
yields in cubic feet. If in the above example the basal area at twenty- 
five years is 57.2 square feet per acre, the reduction per cent is 63 and 
the same prediction of future yield is obtained, which can be modified 
by comparing the number of trees per acre in the same way. 

These illustrations bring out the function of a yield table as dis- 
tinguished from that of merely stating the yields of stands. When the 
total age of any given stand is determined in addition to its volume, 
the rate of growth per year for that stand can then be found, or its past 
yield. But the whole purpose of a yield table is to predict the future 
yields of stands. A standard yield table gives a means of predicting 
this future yield, by indicating first the yield relation as to density of 



416 THE USE OF YIELD TABLES 

the stand in question with the standard yields, the second, the rate of 
growth for future decades, which can be reduced to fit the existing 
stand. 

318. Separation of the Factors of Volume, Age and Area. The 
difficulties surrounding the prediction of 3Melds lie in the fact that this 
requires for any stand the determination of three factors: volume, which 
can always be measured ; age, which can be determined for a given tree 
but is difficult to find for an entire stand of mixed ages; and area, which 
can be measured, provided the boundaries of the age class are known 
or defined. The trouble arises entirely from the mixture of trees of dif- 
ferent age classes on the same area, the overlapping of crowns and root 
spread, and the shifting of total areas occupied by each separate age 
class in successive periods (§ 298 and § 299). Thus two of the essential 
factors, age and area lose their clear definition. These two factors 
are interdependent in such forests. Age classes cannot be confined 
to stands of a single age but must include an age group. The area 
occupied by such a group will be influenced by the number of separate 
ages included in the group. 

It has been shown previously in this chapter that the area occupied 
by a given age class, when determined by mapping, determines the 
relative density of stands whose age is known. The yield table expresses 
an arbitrary standard yield on 1 acre at a given age, representing 
100 per cent density at each age. (This means that the table is accepted 
as standard, but does not necessarily represent the maximum yields 
possible on any acre, which may exceed this standard, by from 15 to 
20 per cent.) When both area and age are determinable for a stand, 
the exact relation as to density or yield when compared with the standard 
can be found for each stand separately. When neither can be found 
with accuracy, they must be found by such means as is possible, and the 
results, while not as accurate, will be serviceable and worth attaining. 
The general method of solving this problem is to work from the known 
to the unknown, accepting averages and approximations when exact 
determination is impossible. 

319. Determination of Areas from Density Factor. One of the 
simplest and most useful applications of this principle is in the deter- 
mination of the area occupied by each of several age classes, whose 
age and volume are known but which have not been or cannot be mapped 
separately. 

The total area of the tract can always be determined. If for any 
reason it is impossible to map the area of each age class, these areas may 
still be found hy proportion if we are willing to assume that the average 
density of the entire stand can he applied separately to each age class. 
While admittedly less accurate than the separate determination of 



DETERMINATION OF AREAS FROM DENSITY FACTOR 41' 



density by classes, yet the total error is probably very small. The 
method is as follows: 

The standard densit\', or 100 per cent, as expressed in the yield 
table, calls for a definite volume per acre, differing with each age. 

The total volume and age of each age class in the forest are known. 

By dividing this volume by the standard volume on 1 acre of the 
required age from the yield table, the area which would be required by 
the age class if stocked at 100 per cent density is found. ' 

The sum of the areas found in this manner for all the age classes 
would be the total area of the forest if the density of stocking were 
100 per cent. 

Since the total area actually stocked is known for this sum or total 
of age classes, but not for each age class separately, it follows that, 
Actual per cent of density for total area 

/Area 100 per cent stockedX 

= rrT — , 100, 

\ Total area / 



and, assuming this per cent for each class, 

. . , , / Area 100 per cent \ 

Area m each age class = I , , , . , 



100 



Vstocked in age class/ per cent of density' 



ILLUSTRATION 
Second-growth Hardwoods in Central New England 



Age. 


Volume. 
Cords 


Yield of 1 acre from 
table. 
Cords 


Area of 100 per cent 

stocked. 

Acres 


20 
30 
40 
50 


1738 
5593 
3854 
1008 


15.80 
29.75 
39.63 
48.00 

Total 


110 

188 
97 
21 




416 acres 



Actual area 624 acres. 



416 
Density per cent —- = 663 which will be assumed to apply to each of the four 
024 

age classes represented. 

To determine the area in each age class; 

100 
Ratio to fully stocked area — = 1.5. 
• 661 



418 



THE USE OF YIELD TABLES 



Age class. 
Years 


Area 100 per cent 

stocked. 

Acres 


Actual area in age 
class. 
Acres 


20 
30 
40 
50 


110 

188 

97 

21 


165 
282 
145.5 
31.5 


Total 


416 


624 







This method of obtaining the area of separate age classes makes 
possible the prediction of yields from yield tables based on age for 
long periods with considerable accuracy, where without such separation 
this would not be possible and yields could be predicted only for the 
current decade or two. 

320. Application to Forests Having a Group Form of Age Classes. 
Forests composed of species which are intolerant and fire-resistant 
tend to form groups of approximately even age. A yield table based 
on age can be obtained for such species, which will serve as a 100 per 
cent standard. But it is very difficult to separate the forest itself into 
its component age classes by mapping the areas which they occupy, 
and equally difficult to determine in a practical manner the average 
actual age of the stand on such areas even if mapped. But the forest 
can still be separated into these age classes based on area and age, 
permitting the application of this yield table to predict its growth, 
provided proper use is made of the laws of averages. (In timber estimat- 
ing, it is permissible to employ averages known to be subject to error 
because it is not practicable to attain mathematical accuracy on account 
of expense.) 

The problem here is, 

1. To determine the trees which belong to each age class so that the 
volume of the class may be found. 

2. To determine the age of the age class. 

3. To find its area. Given the first two of these elements, the 
method of finding the third has already been shown (§ 319). 

By reference to § 275 it is seen that diameter is an indicator of the 
age of trees, but that a given age class will include a wide range of diam- 
eters. Where stands are composed of trees of many difTerent ages so 
that it is not possible to ascertain the age of a given stand by felling 
one or two trees, nor to map the separate areas in the forest which are 
occupied by these age classes, the only alternative in obtaining age 
is through the use of average diameters. The diameters can be meas- 



VOLUME AND AREA FOR TWO AGE GROUPS 419 

ured. In timber estimating, a stand table can be made giving the range 
and distribution of diameters in the stand. The substitution of diam- 
eters for ages thus furnishes a means of separating age classes in forests 
of mixed ages. 

Choice of Methods. There are tnree gradations in the possible 
applications of this method. 

1. Diameter is used merely to determme the age of an average tree, 
but the forest is separated into actual age classes as nearly as possible, 
rather than diameter classes (§321). 

2. Diameter is used as the basis of separation into classes, whose 
average age is then determined on the basis of these diameters (§ 323). 
These, as shown (§275), are not true age classes since they do not 
include all the trees of a given age. 

3. Diameter is substituted altogether for age, and the total age of 
trees is not determined for these classes, but current growth is predicted 
merely for trees of given diameters for short periods. This method is 
discussed in Chapter XXXII. 

The use of diameter to indicate total age is most reliable when applied 
to large areas and numbers and to forests of many age classes, for species 
and stands whose actual and economic age agree, i.e., which usually 
do not show a period of suppression. 

321. Determination of Volume and Area for Two Age Groups on 
Basis of Average Age. While the method to be described is limited 
in its application to two age groups, yet even this subdivision will be 
found of great value in Mensuration and Regulation. In the French 
many-aged forests, but two groups are made in timber above exploit- 
able size. In our forests, when under management, the subdivision 
into two groups will be equally effective. 

In natural stands containing decadent timber, three groups are 
needed instead of two, for timber above the minimum diameter. These 
may be termed " young merchantable," " mature " and " veteran." 

In the Western yellow pine stands for which this method was 
developed, it was possible to separate the young merchantable timber 
by the appearance of bark into a class termed " Blackjack," leaving 
the remaining yellow pine timber for separation into mature and 
veterans. In forests where this cannot be done, it is possible to first 
separate the young merchantable timber on a diameter class basis, 
leaving the larger mature and veteran timber for division by this method. 
Where the forest is cut over, and but two age classes are required, 
the method will separate the young merchantable from the mature 
timber. The three steps in this method are as follows: 

1. A standard yield table based on age for even-aged stands can 
be made the basis of separation of the forest into two age groups. This 



420 THE USE OF YIELD TABLES 

yield table can be constructed by standard methods from selected plots 
in the groups of which the forest is composed. From this yield table 
two ages are chosen, representing respectively the younger and the 
older age class. The development of the normal stand as indicated 
by its current and its mean annual growth is the basis for this choice 
of ages. 

2. The ages thus chosen from the yield table must then be correlated 
with a given diameter since it is impossible, in the forest, to determine 
either the age or area of age classes directly. 

This requires a table of diameter growth on the basis of age, for the 
species and site (§ 267 to § 269) based on a sufficient number of trees 
to insure a reliable average. Age is the direct basis of this curve, and 
not diameter (§ 275). From this table, the diameter sought is indicated, 
for each of the two age classes. 

3. The total volume on the area contained in the two age classes 
can be separated into the volume in each age class, by means of these 
two trees of average diameter, representing average age of each class. 
This requires: 

(a) That the average volume contained in a tree of this average 
diameter be found. For this purpose, a curve of average height based on 
diameter is constructed for the site (§ 209). With the height of a tree 
of the required diameter thus indicated, its volume is found from the 
standard volume table for the species and region. 

(b) That the number of trees with this average volume be found 
for each age class, which is required to make up the total volume of the 
combined group. This number, multiplied by the average volume 
will give the volume of each age class. 

This solution is simple, when the total number of trees and their total volume 
are known. Deducting a given number of trees of a given average volume from the 
group leaves a residual volume, which is equivalent to a fixed number of trees of the 
average volume for the remaining group; i.e., with total number, total volume, and 
the average volume of each tree of two groups fixed, there can be but one solution by 
which the number in each group, and consequently the sum of their volumes equals 
the required or existing estimate or total in the stand. 

If a; = number of trees in younger group; 
y = number of trees in older group ; 
a = volume of average younger tree; 
b = volume of average older tree. 
Then 

x-\-y = total number of trees in stand, c 
and 

ax+by = total volume of stand, d. 

If all the trees c had the volume a then instead of a total volume d, 

ax+ay = ac, 



APPLICATION OF RESULTS TO FOREST 421 

The difference between this volume and the total actual stand is d—ac and repre- 
sents the surplus volume in the older trees, of which there are y. The difference 
in volume for each tree is b —a, and for all of the older trees is {b — a)y. 
Then 

{b — a)y = d—ac; 
and 

d—ac 
b — a 
while 



Having the values, or number, of each group x and y, the total volume is obtained 
by multiplying this number by the volume of the average tree for the group. 

Illustration, Western Yellow Pine. 

Total volume in group (d) =27,042,800 feet B.M. 
Total number of trees (c) =44,423. 
Age of older trees, veterans, chosen as 300 years. 
Age of younger trees, mature, chosen as 200 years. 
Diameter, from curve of growth, veterans, 27 inches. 

mature, 20.7 inches. 
Volume of average tree of this size, veterans 805 feet B.M. 
mature, 340 feet B.M. 
Then 

(1) 340x +805?/ = 27,042,800 feet B.M. 

(2) 340x+340y = 340f. 

= 15,103,820 feet B.M. 
Subtracting (2) from (1) 

465j/ = 11,938,980 feet B.M. 
y = 25,675 trees; 
a; = 18,748 trees. 
Volume of younger class = 6,374,320 feet B.M. 
Volume of older class =20,668,375 feet B.M. 

322. Application of Results to Forest by Use of Stand Table and 
Per Cent. It is not necessary that a 100 per cent tally of the number 
of trees, and total volume for the site be obtained, but only that the 
stand table (§ 188) from which the determination is made be representa- 
tive of the total area. 

If in the timber survey, 5 per cent of the area is covered and assumed 
to represent the average stand, the total count of trees on this 5 per 
cent and the total estimate on the strip, give the data needed. If, 
in turn, but 10 per cent of the strip itself or i^ of 1 per cent of the total 
area is tallied, and this per cent gives the run of sizes of the timber 
without reference to its density of stocking, the data are still sufficient. 

To obtain the separation of the total stand by means of the data 
from the smaller area counted, the volume of each age class is first 
expressed as a per cent of the total. These per cents are then applied 
to the total estimated volume on the entire area. 



422 THE USE OF YIELD TABLES 

In the above case, the per cents are: 
Veterans 76.4 
Mature 23 . 6 
The total stand is 2,583,940,000 feet B.M. 
The stand of veterans is then 1,974,130,000 feet B.M. 
and of mature is 609,810,000 feet. B.M. 
To secure this division, a Uttle over 1 per cent of the total stand was tallied and 
estimated for the basic data, while the total estimate was secured by ocular means 
(§ 208) (Coconino National Forest). 

323. Determination of Volume and Area for Age Groups on Basis 
of Diameter Groups. Where the second alternative is chosen (Method 2, 
§ 320) to obtain the separation of age classes, namely, diameter rather 
than age, the following changes in procedure are necessar3^ 

1. The volume of the so-called age classes is directly obtained from 
a stand table, in which the number of trees of each diameter class must 
be shown. 

2. The diameter of the average tree is obtained by first finding the 
average volume for the group, and second, the tree of this volume 
from a local volume table based solely on diameter, which is obtained 
from a curve of average heights and a standard volume table. 

3. The age of a tree of this average diameter is then found, not 
from the yield table as before, but from the curve of growth based on 
diameter, which gives directly the ages of trees of given diameters. 
The ages indicated will be those of the respective age groups into which 
the forest has been separated. As indicated, this method works back 
from diameters to age, while the first is based on age directly. 

By either of these methods, the area in each age class may now be 
found by following the procedure described in § 319. The age, and 
consequent normal yields for 1 acre at these ages, have been determined 
for each age class. The total normally or 100 per cent stocked area 
can be found, and from this the reduction per cent and the area in each 
age class. From the reduction per cent an empirical yield table can 
be computed, which will be used as the basis for predicting the yields 
of the forest or site class as a whole (§ 250). 

Since the above-described methods of determining areas of age 
groups are based primarily on the factor of relative density of the stands 
as determined by volume, they apply only to the age groups which 
have already grown to merchantable sizes. The problem of determin- 
ing the area of immature age classes is treated . in § 348, and must be 
considered in working out a plan for growth predictions for any large 
area, in connection with the above methods. 

324. The Construction of Yield Tables Based on Crown Space, for 
Many-aged Stands. The above methods depend upon the construc- 
tion of yield tables from plots whose average age is determined, so that 



THE CONSTRUCTION OF YIELD TABLES 423 

the yields are given as for even-aged stands. Since it is seldom that 
any species is so distributed in age classes and so free from major sources 
of damage as never to be found in stands of even age, plots based on 
age can be obtained under a greater range of conditions than is commonly 
admitted. 

But when this method is apparently impracticable, there remains 
one possibility for constructing a yield table based on age, which although 
far from being accurate, is based on a fundamental law of growth of 
stands. It was shown in § 274 that as trees develop, they require 
increased crown space, and that this expansion of crown can be attained 
only by the reduction of numbers of trees per acre. 

The diameters of crowns of trees is an index of the growing space 
which they require though it seldom exactly measures this space. But 
if it can be shown that the space occupied by trees of different diameters 
is proportional to the diameter of their crowns, the relative number 
of trees per acre of different diameters which can stand on an acre 
can be determined. 

To obtain such data, crowns can be assumed as circular in shape, 
(though the actual shape varies according to the light and growing 
space available, especially in hardwoods), and that the space occupied 
by each crown is in proportion to the square of its diameter or width 
in feet. 

Measurement of Width of Crowns. To determine the average width 
of crown for trees of different diameters, two men may work together. 
One stations himself behind a plumb-bob suspended from a pole so to 
hang clear from a height of about 8 feet. He lines in the second man 
at a point below the outer edge of the crown of the tree, whose width is 
then measured on the ground to the point intersecting the opposite 
edge of crown. For this purpose a pole, marked in feet, can be used. 
The distance measured must be at right angles to the lines of sight. A 
record is made of the D.B.H. and crown width. ^ 

Areas of Crowns. To obtain a true average of crown area, each 
crown width must be squared. The sum of the areas so obtained for 
each diameter class is divided by the number of trees in the class, to 
get the average area of the square for that class. The square root, 
or side of this square is the average width of the crown for the class. 
Now, if it be assumed that the space occupied by this diameter squared 
represents the actual growing space required by the tree, the number 
of trees per acre for the diameter class is found by dividing the area 

■' No effort need be made to obtain the area of each crown by two or more measure- 
ments or by plotting the projected area of the crown. Reliance is placed on a large 
number of measurements of one diameter, rapidly and accurately taken, to obtain 
the true average diameter of crowns for each D.B.H. class. 



424 THE USE OF YIELD TABLES 

of one acre, 43,560 square feet, by this area. This method is employed 
in finding the number of trees per acre required to plant an acre, if 
spacing is 4, 6, 8 or 10 feet apart in both directions. 

Density of Crown Cover. In actual stocking, the absolute number 
of trees cannot be so simply determined. As crowns tend to adjust 
themselves to light, they depart from a circular form, and the circular 
spacing itself may permit of more trees per acre than the square. The 
relation of the area of an inscribed circle to a square is .7854. That 
of an inscribed circle to a hexagon is .9018. 

If either of these relations is consistently maintained, the total 
number of trees per acre for full crown cover may differ, but the relative 
number, for trees of different diameters will remain constant. From 
the number so found, a curve of number of trees per acre based on diam- 
eter can be plotted. This is a standard, intended to show relative, 
not absolute, numbers. For instance, if the number per acre from 
such a table for a given diameter is 400 trees, a stand of 200 trees per 
acre of this average diameter would be 50 per cent of the standard. 

Two factors interfere to prevent the satisfactory application of such 
a table in predicting yields. First, the number of trees in fully stocked 
stands does not always decrease in direct proportion to their increase 
in crown space. In tolerant species, a great over-lapping and suppres- 
sion of crowns occurs, doubling the number of trees per acre over the 
theoretical number indicated by the spread of crown, while in over- 
mature stands, the increasing demand for light and moisture reduces 
the stand per acre below that indicated by the crowns. The relation 
is therefore not consistent except within rather narrow limits of age 
and species; and yields based on this assumption will be excessively 
large for over-mature age classes. 

The second factor tends to offset the first in stands not fully stocked — 
this is the tendency (§301 and § 316) to improve the degree of stocking 
with age. When a stand of a given age has only the number of trees 
required for one twice this age, its rate of mortality will be very much 
less since each tree has more than enough room to survive. Hence 
the assumption, in stands not fully stocked, that the growth of a stand 
can be predicted by determining the per cent which the number of 
trees now in the age class bears to the normal number, will not be 
borne out, but better results will be obtained. 

Method of Construction of the Yield Table. In stands which 
possess a full crown cover, but whose age classes are distributed in 
many-aged form, the rate of mortality may be assumed to hold for 
all classes. An illustration of the above method of constructing a 
yield table for yellow poplar in Tennessee is given below.^ 
1 Based on data collected by W. W. Ashe. 



METHOD OF CONSTRUCTION OF THE YIELD TABLE 



425 



TABLE LXIV 
Trees per Acre Based on Crown Space 



D.B.H. 


Diameter of crown. 


Area of crown based on 


Trees per acre. 


Inches 


Feet 


Square feet 


Number 


7 


11.0 


121 


360 


8 


11 6 


134 


325 , 


9 


12.4 


154 


283 


10 


13.3 


177 


246 


11 


13.7 


187 


233 


12 


14.4 


207 


210 


13 


15.1 


228 


191 


14 


15.8 


249 


175 


15 


16.5 


272 


160 


16 


17 2 


295 


148 


17 


17.9 


320 


136 


18 


18.6 


346 


126 


19 


19.4 


376 


116 


20 


20.0 


400 


109 


21 


20.7 


428 


102 


22 


21.3 


453 


96 



The above data must now be correlated with age. The steps are 
as follows: 

1. From a curve of age based on diameter, the diameters at each 
five-year period are found, and the number of trees per acre, formerly 
based on diameter, are then interpolated for the fractional diameters 
corresponding to these exact ages. 

2. From a curve of height growth based on age the height of the 
average tree is found. 

3. From diameter and height, the volume of each tree is taken 
from a standard volume table (§ 288). 

4. The yield per acre at each age is the product of the number of 
trees per acre and this average volume. 

The application of this method is shown in Table LXV, p. 426. 

325. Application of Method to Many-aged Stands. To apply this 
standard table to the many-aged forest for the prediction of yield, 
the same principles are used as were described in § 316. But in this 
case, the number of trees in given diameter classes is the basis of comparison 
to determine the reduction per cent or density factor. 

It makes no material difference whether the standard table above 
illustrated exactly represents the true or actually possible normal yield 
of a pure, even-aged fully stocked stand, provided it approximately 



426 



THE USE OF YIELD TABLES 



indicates the proportional yields at different ages, correlated with the 
proportional falling off in numbers of trees per acre at these ages, both 
factors correlated with diameter of the average trees, for it is evident 
that in such a forest no stands will be found which are pure, even-aged 
or fully stocked over any large area; hence the use to which the table 
is put must be solely as a standard to he discounted by a reduction per 
cent. 

TABLE LXV 

Yields of Cordwood, for Yellow Poplak in Tennessee — Based on Crown 
Space and Volumes of Trees of Given Ages 



Age. 
Years 


D.BH 
Inches 


Average 

Height. 

Feet 


Volume * 

in cords of 

160 cord feet. 

Cords 


Trees 
per acre 


Yield 

per acre. 

Long cords 


40 


10.5 


78 


0.148 


237 


35.1 


45 


11.8 


83 


.198 


214 


42.6 


50 


13.0 


87 


.254 


191 


48.5 


55 


14.2 


91 


.317 


172 


54.5 


60 


15.4 


94 


.381 


155 


59.0 


65 


16.5 


97 


.445 


141 


62.7 


70 


17 5 


101 


.511 


130 


66.4 


75 


18.4 


104 


.569 


121 


68.8 


80 


19.3 


107 


.630 


114 


71.8 


85 


20.2 


110 


.693 


108 


74.8 


90 


21.0 


113 


.755 


102 


77.0 


95 


21.8 


115 


.825 


97 


80.0 


100 


22.5 


117 


.880 


94 


82.7 



* From volume table 5, p. 22, Bulletin 106, Yellow Poplar in Tennessee, W. W. Ashe, State 
Geological Survey of Tennessee, 1913. 

The age of stands, by this method, is assumed as the age of trees 
of given diameters. To determine this age, for each diameter class, 
a curve of growth is required in which ages are averaged on the basis 
of diameter (§ 276). Otherwise the ages of trees of the larger classes 
will be over-estimated. 

To apply this yield table for the prediction of yield in the forest, 
a large area must be considered; otherwise the assumed correlation 
between age and diameter will not hold good. The stand table (§ 188) 
for this area must show the number of trees of each diameter class in 
the forest. 

One of the principal services rendered by such a table is its indication 
of the probable rate of loss of numbers, which is a most difficult problem 
to solve by any other method. 



YIELD TABLES FOR STANDS GROWN UNDER MANAGEMENT 427 

In applying such a table, it can be assumed that the mortality in 
the forest will be at the proportional rate indicated by the table. The 
prediction of yields will then be based on a stand table giving the number 
of trees in each diameter class. Several methods of applying the 
standard table are possible, as 

1. Base the prediction upon the total number of trees in each diam- 
eter class or group. The per cent of reduction in numbers is obtained 
from the table. This per cent is applied to the stand in the forest, 
and the future growth obtained by computing the future volume of 
the remaining trees, as shown in the illustration. 

2. Base the prediction upon yields. The number of trees in each 
diameter class is divided by the number per acre in the standard table. 
This gives the area normally stocked by that class, from which its future 
yield is taken directly from the standard yield table. This area forms, 
of course, but a small per cent of the forest, and is the total area occupied 
by trees of the diameter class. 

The forest can be divided into age classes, based on diameter, and 
the area occupied by each of these age classes obtained as described 
in § 316. 

At best, it can be seen that this substitution of standard yields 
based on growing space per tree is a makeshift compared with determin- 
ing these relations from even-aged plots in which the factors of site, 
tolerance and soil at different ages are directly measured. 

326. Yield Tables for Stands Grown under Management. European . 
experience with stands grown under management has shown, first, 
that the best results and heaviest total yields per acre are obtained 
by several thinnings at frequent intervals, in which not only the trees 
which would otherwise die before the next cutting are removed, but the 
remaining crowns are freed from competition. 

Second, that the proportion of the total yield removed as thinnings 
under this system may equal one-third or more of the total yield. 

Third, that the diameter growth of the surviving trees can by proper 
thinnings be sustained at a uniform rate until the final crop is cut. 
The development of each tree in the stand proceeds actually at the rate 
of growth of a dominant tree which maintains its crown spread through- 
out its life. 

Even where second-growth stands have sprung up, in this country, 
and reached sizes suitable for logging, they have usually received no 
care in the form of thinnings. Stagnation sets in on many of these 
stands, especially with conifers on old fields, and the diameter 
growth of the whole stand suffers. This occurs even in plantations 
on which thinnings have been neglected. 

The actual yields and sizes which may be grown on such stands 



428 THE USE OF YIELD TABLES 

under sustained management and thinnings may be roughly approxi- 
mated by measurements taken on natural stands not under management, 
by the method just discussed, of computing the number of trees per acre 
for given diameters. The rate of diameter growth should be that of 
trees now dominant in the stand. This gives the age of the diameter 
classes. The approximate amount of material yielded by thinnings in 
such a forest may also be roughly predicted by noting the number of 
trees which drop out of the stand at each decade, and computing their 
average diameter and volume. 

By establishing permanent plots, re-measured at intervals of 5 
or 10 years, and properly thinned, data will finally become available 
showing not merely the yield of stands grown under management, at 
final cutting, but the total yield including thinnings. The absence 
of such stands precludes the construction of yield tables on this basis 
at present and justifies efforts to predict such yields by means of crown 
spread and number of trees per acre in normal stands. The nearest 
approach to such yield tables is found in tables constructed from second- 
growth stands, or plantations, but it is seldom that these stands have 
been repeatedly and properly thinned, hence the yields shown merely 
indicate a normal possibility for fully stocked, wild stands. 

References 

The Measurement of Increment on All-aged Stands, H. H. Chapman, Proc. Soc. 

Am. Foresters, Vol. IX, 1914, p. 189. 
Yield Table Methods of Arizona and New Mexico, T. S. Woolsey, Jr., Proc. Soc. Am. 

Foresters, Vol. IX, 1914, p. 207. 
Yield in Uneven-aged Stands, Barrington Moore, Proc. Soc. Am. Foresters, Vol. 

IX, 1914, p. 216. 



CHAPTER XXX • 
THE DETERMINATION OF GROWTH PER CENT 

327. Definition of Growth per Cent. Growth per cent is an expres- 
sion of the relation between growth and volume. 

Current growth per cent is the relation of growth during a given 
year to the volume at the beginning of the year. 

Periodic growth per cent is the relation of the growth during a period, 
to a basic volume, which may be taken as the mean or average volume 
for the period (§ 328), but is usually that at the beginning of the period. 

Mean annual growth per cent is the per cent which the mean annual 
growth (§ 245) for a given age bears to the total volume at that age, 
and represents the average rate of growth per year, at which this volume 
has been produced. Growth per cent requires for its determination 
a knowledge of two factors, the growth for a period and the volume 
upon which this growth was laid. The primary purpose for which 
growth per cent is utilized is to test the maturity or ripeness of individual 
trees and of stands of timber. Those trees or stands which show the 
lowest per cent of increment on their present volume compared with 
other trees or stands, should be selected for cutting. The object of 
such selection is to withdraw from the forest the greatest possible volume 
of wood capital, while at the same time reducing the volume of expected 
growth by the smallest possible amount. If carried out, the effect is 
to transform the forest capital from a condition in which the ratio of 
growth to volume is low, to one in which this ratio is materially increased 
for the forest as a whole. 

On individual trees the difference in volume or growth for the decade 
may be found by analysis (§ 287 and § 288). For stands, the difference 
is taken from yield tables for the decade. In each case one year's 
growth is one-tenth of the growth for a decade. The growth per cent 
of average test trees is frequently assumed to be that of the stand. 

328. Pressler's Formula for Volume Growth Per Cent. To deter-" 
mine growth per cent as a means of judging the ripeness or maturity 
of stands or trees, the same methods apply whether the unit is the tree 
or the stand. Since volume growth is measured for periods of a decade, 
the growth for one year is found by division. Let n equal the period 
representing a decade. This may be a longer or shorter period if neces- 

429 



430 THE DETERMINATION OF GROWTH PER CENT 

sary. Let V equal volume at present, and v equal volume n years ago. 

V — v 

Then growth for one year equals . If it is assumed that this 

n 

growth for n years is laid on in equal annual installments, then the growth 

so obtained is considered that of the current year or for any year during 

the period. 

If the growth per cent is obtained on this basis, the result will vary 

according to the year in which the volume of the stand is taken as the 

basis. If for ten years ago, then the formula is. 



/ V — v\ 
Growth per cent = I — I 100. 

\ vn / 



But if the per cent is desired for the last or present year, 
Growth per cent= ( -r- — ) 100. 

For an average year midway of the period, the capital or volume is 

V+v 
2 ' 
and growth per cent is 

V-n 
n ^^^^ (V-v\ 200 



V-\-v \V-\-v/ n 

~2~ 

This is known as Pressler's formula. 

329. Pressler's Formula Based on Relative Diameter. Further modifications 
of this formula by Pressler are intended to reduce it to terms of diameter so that it 
may be appUed to measurements on standing trees taken at B.H. If height and form 
factor do not change, then 

_ / D'--dA 200 

In this formula D is the present D.B.H. and d is the diameter Ji years ago. D—d 

is then designated as a and — is called the relative diameter. By making — =q, 

a a 

and substituting aq for D, and a{q — \) for d, he reduced the formula thus to 

^/ q2-(q-l)2 \200 

^ W+(<7-l)V « ' 
for which expressions values are computed in a table. 

To use this table the present diameter D is divided by twice the width of the 
rings in the period n, thus indicating the relative diameter. The values in the table 
give the per cent of volume growth /or the period. This is then divided by the num- 
ber of years in the period to get the current annual growth per cent.i 

1 This table is given in Principles of American Forestry, Samuel B. Green, John 
Wiley & Sons, N. Y., 1903, p. 178. 



SCHNEIDER'S FORMULA FOR STANDING TREES 431 

Further modifications of this formula are discussed in Graves' Mensuration, pp. 
306-7. 

330. Schneider's Formula for Standing Trees. The most con- 
venient formula for testing the growth per cent of standing trees is 
known as Schneider's formula, developed in 1853 by Professor Schneider, 
Eberswalde. This formula is applied at B.H. and requires the deter- 
mination of diameter, D, at that point, and the number of rings in the 
last inch of radius, n. Then 

400 

The following description of the derivation of the formula is taken from Graves' 
Mensuration, p. 308. 

If n represents the number of rings in the last inch of radius at breast-height, 

then the periodic annual growth during n years is - inches. Let the present diameter 

n 

2 

be represented by D, then the diameter last year was D and the diameter at the 

n 

2 
end of one year from now will be D + -. 

n 

■irD^f 

The present volume of the tree is — ^ — , that of one year ago was 
The growth for the last year is then 

^D%f TT / 2y ThfUP _ 4 

4 4 \ n/ 4 \ n n= 

The growth per cent is: 

TrDVlf 7rhf/4D 4\ 

: — = 100 : p. 

4 4 \ n nV ^ 

400 400 

2 2 

If the growth be calculated on the basis oi d+~ instead of d — , then the follow- 

n n 

ing formula will result: 

400 400 

The average between the two formulae is taken, namely, 

400 

Inasmuch as Schneider's formula assumes that there is no change 
in height and nor change in form factor, the results are very conservative. 



432 THE DETERMINATION OF GROWTH PER CENT 

An attempt has been made to adapt the formula to rapid-growing 
trees by substituting other values for 400, but the resulting formulae 
have little practical value. 

331. Use of Growth Per Cent to Predict Growth of Stands. Growth 
per cent is sometimes used to determine the growth of trees or stands, 
by both the standard methods, that of prediction, and of comparison. 
It is not well adapted to secure accurate results by either method. 
Owing principally to the variability of the per cent relation, and its 
direct dependence on and derivation from the two factors, volume and 
increment, the problem of reversing this process and deriving increment 
from growth per cent is apt to lead to error through a mistake either in 
choosing the basis of volume for deriving the per cent figure, or in 
applying this figure in turn to the wrong volume basis. 

The method of prediction of growth by means of growth per cent 
consists of determining this per cent for a stand, either from sample 
trees (§ 241) or by direct use of yield tables or other methods of measur- 
ing the past growth for a decade. 

Schiffel states, " If in any period of life the current annual incre- 
ment per cent of a tree is to be calculated, it would be contrary to nature 
and incorrect to relate the increment to any former dimensions or 
volume, but it must be related to the dimensions or volume of the previ- 
ous year." 

The formula, growth per cent = ( -tt-t— ) — when n=10 years, 

\ V + vj n 

bases growth per cent on volume five years ago, and is correct as an 
average per cent of the past ten-year period. If applied to the next 
decade, and based on V, or present volume, it assumes an increase in 
growth for this period. Wlien this per cent is applied only to the current 
year, and is based on V the per cent is more conservative. 

While individual trees are growing rapidly in diameter, as dominant 
trees, their growth per cent for a time falls less rapidly than that of 
slower-growing trees. In even-aged stands, growth on individual trees 
is proportional to their diameters. Growth per cent in area is about 
twice the per cent of diameter growth. If determined for the trees 
which will be retained under management, this relation of growth to 
volume may be fairly consistent in such even-aged, thinned stands. 
Hence sample or average trees may give a close indication of the growth 
per cent or present status of the stand. But the assumption that this 
growth per cent will continue to be laid on annually breaks down at 
once; hence the real assumption and the only one possible, if growth 
per cent is to be applied for predictions, is that the volume indicated 
by this per cent will continue to be laid on annually. And this in turn 
is inaccurate. 



GROWTH PER CENT TO DETERMINE GROWTH OF STANDS 433 

The sources of inaccuracy in this method are: 

1. Predicting the volume growth of a stand from that of one or two 
selected or average trees. The growth per cent of a stand is practically 
always less than that of the average trees which survive, due to loss 
of numbers and falling growth rate of the suppressed class. 

2. Applying a growth per cent obtained from a past period on a 
smaller volume, to the present volume of tree or stand, under the assump- 
tion that not only will the rate of growth in volume continue the same 
but the per cent will remain unchanged, when, as shown, growth per 
cents always fall as wood capital increases. 

3. Assuming that the growth per cent as derived from average 
trees, or even from sample plots, will apply to larger areas and to dif- 
ferent proportions of age classes in mixture, when in fact, so doubly 
sensitive is this per cent relation, that any difference in average age 
and volume between the forest and the sample areas will i*esult in a 
large error in determining the true weighted per cent by this means. 

The possible errors may be illustrated as follows : 

From a yield table for White Pine ^ the actual known yields are, . 

At 30 years 3750 cubic feet 

40 years 6590 cubic feet 

50 years 8035 cubic feet 

60 years 9075 cubic feet 

By Pressler's formula, the current annual growth per cent for these decades is, 

30 to 40 years 5.5 per cent 

40 to 50 years 2.0 per cent 

50 to 60 years 1.2 per cent 

If the growth for the decade from thirty to forty years be taken to indicate the 
current growth in the fortieth year, of 284 board feet, this gives a current growth per 
cent for that year on 6590 board feet, of 4.3 per cent. Assuming that this growth 
per cent will continue for the next decade, we have a total increase of 43 per cent or 
2834 board feet. The actual growth is 1445 board feet. The error is 96 per cent 
excess. 

Such errors are the result of use of the growth per cent, even when the basic 
data are correct. The errors may be greatly increased when growth per cent is 
obtained from single trees and the losses in the stand are ignored, since too high a 
current growth per cent will be obtained. 

332. Use of Growth Per Cent to Determine Growth of Stands by 
Comparison with Measured Plots. The only merit which growth per 
cent has as a method of determining growth lies in the possibility of 
using it as a means of comparison. Since per cent does not express 

^ Forest Mensuration of the White Pine in Mass., H. O. Cook, OfRce of State 
Forester, 1908, p. 21. 



434 THE DETERMINATION OF GROWTH PER CENT 

absolute quantity but a relation, the assumption is that this relation 
once established for a given stand will apply to other stands of a similar 
character but differing in area and total volume. Growth per cent 
on sample plots could for instance be applied to determine the annual 
growth on the stand within which they are located. 

In so far as it can be known that the relation between the volume 
of the larger area and the growth on this area is the same as on the stand 
sampled, the method is obviously correct. The error lies in applying 
such growth per cent figures to stands or areas on which this relation 
is not the same, because the average age, thrift, or other conditions, 
differ from the sample area. The simplicity of assuming that growth 
per cent for a sample tree, or for a sample plot, can be applied to large 
areas has led to its use as a substitute for sound growth data in many 
instances. No such short cut will actually measure the growth on a 
forest comprising many stands of different ages, site qualities, and 
densities of stocking. 

333. Use of Growth Per Cent in Forests Composed of All Age 
Classes. Growth per cent is a direct expression of current growth in 
its relation to past or total volume. Hence it varies with the current 
growth curve. Current growth per cent is equal to mean annual 
growth per cent in the year in which the mean annual growth culmi- 
nates (§ 245). 

In a forest composed of stands of all ages, or in a stand composed 
of trees of all ages, equally proportioned as to area or ultimate yield, 
and under management, the current growth per cent for the whole 
forest or the whole stand, when weighted by volume of each age or tree 
class, will be equal to the mean annual growth per cent for every year, 
since there is no change from year to year in either of the two factors, 
total volume or increment, which determine it. 

For such a forest the average growth per cent can be found separately 
for each diameter class. By weighting each per cent according to the 
volume of the trees in this class for the stand, a composite per cent is 
obtained which shows the present status of the forest, and is applicable 
in predicting its growth. But accurately to determine this per cent, 
the growth itself must first be found on the trees or plots measured. 
If in determining this growth, the future factors are really considered, 
the numbers reduced, and the rate of diameter growth and probable 
suppression taken into account, the result is a quantitative statement 
of growth for the next decade or two instead of for the past decade. 
This prediction of growth, on a few acres or a small per cent of the stand, 
can then be reduced to the form of a per cent of present volume, and 
applied, in this form, to the remaining stand as a convenient means of 
computing growth on the total area. 



GROWTH PER CENT IN QUALITY AND VALUE 435 

334. Growth Per Cent in Quality and Value. Growth in money 
value of a stand is treated in Forest Valuation.^ This depends upon 
the three factors mentioned in § 244, namely, increase in volume, in 
quality, and in unit price independent of the other two factors. The 
growth in quality differs from that in volume, since it tends in a measure 
to raise the value of the previous growth, especially when this increased 
quality is due to increased dimensions. Per cent increase in value is 
usually computed as an annual per cent found by dividing the periodic 
per cent by the years in the period, and is applied to the volume at 
the beginning of the period, thus showing simple interest on the initial 
value. When thus expressed, the per cent of increase is made up of 
the sum of the per cents due to each of the three separate factors. 
For young and immature timber, growth per cent in volume forms the 
chief element of increase, but as the trees reach maturity this diminishes, 
and is greatly exceeded by per cent increase in price due to quality, and 
to unit prices — so that the per cent of increment in value may con- 
tinue for a much longer time than that of volume. 

The growth in quality of a stand can be measured by the use of 
graded log tables (§74) or graded volume tables (§165) provided it 
is carefully ascertained that these tables apply to the trees in the stands 
to be measured, at the successive ages. 

References 

A Practical Application of Pressler's Formula, A. B. Recknagel, Forestry Quarterly, 

Vol. XIV, 1916, p. 260. 
Table for Determining Financial Increment Per Cent for Trees Based on their 

Market Values, Erling Overland, Translated by Nils B. Eckbo, Forestry Quar- 
terly, Vol. V, 1907, p. 36. 
Increment Per Cent, Schiffel, Centralblatt f. g. d. Forstwesen, Jan., 1910, p. 6. 

Review, Forestry Quarterly, Vol. VIII, 1910, p. 377. 
Hilfstafel zur Zuwachserhebung, Forstwissenschaftliches Centralblatt, Apr., 1911, 

p. 200. Review, Forestry Quarterly, Vol. IX, 1911, p. 321. 
Relative Increment of Tree Classes, Review, Forestry Quarterly, Vol. IX, 1911, p. 

633. 
Zuwachsuntersuchungen an Tannen, AUgemeine Forst- und Jagdzeitung, Sept. 

1907, p. 305. Review, Forestry Quarterly, Vol. V, 1907, p. 431. 
Ueber Zuwachsprocent, Centralblatt f. d. g. Forstwesen, Jan., 1910, p. 6. Review, 

Forestry Quarterly, Vol. VIII, 1910, p. 377. 

1 Forest Valuation, H. H. Chapman. John Wiley & Sons, N. Y., 1915. 



CHAPTER XXXI 

METHODS OF MEASURING AND PREDICTING THE 
CURRENT OR PERIODIC GROWTH OF STANDS 

335. Use of Yield Tables in Prediction of Current Growth. The 

current growth of stands for short periods can always be predicted 
with greater acciu-acy than for long periods. Not only can the present 
condition of the stand be gaged, as to species, numbers, crown density, 
form, thrift and rate of growth in immediate past, and this information 
applied in predicting the rate at which growth will continue, but the 
inevitable changes, some of them unforeseen, which will occur in the 
future to modify this rate of growth, take place at a rate which bears 
a close relation to the length of the period of prediction. 

Only when the net results of all the various factors which produce 
yields have been measured on stands after they have passed through 
the period is an approximate degree of accuracy obtained for long periods, 
hence the use of yield tables based on age. It follows that for the pre- 
diction of current growth for short periods on existing stands, the net 
current growth shown by the above yield tables, reduced on the basis 
of age and relative density to apply to the stand in question, is the 
best basis of growth prediction even for these short periods. 

336. Method of Prediction Based on Growth of Trees, with Cor- 
rections for Losses. In endeavoring to use these yield tables for 
stands which differ greatly from the normal in number of trees per acre, 
density of crown cover, form or distribution of age classes, and com- 
position of species, it is often difficult to find or make a table which will 
apply to the stand even when corrected for density. In such cases, 
a direct measurement of the stand may be resorted to instead of a com- 
parison with a standard yield. The growth of any stand of whatever 
character, for the next decade, will be the sum of the growth in volume 
of the trees which survive till the end of this period minus the loss of 
the total volume of the trees which do not survive ( § 252) . The elements 
which give stability to this method are a knowledge of the exact pres- 
ent number and diameter of the trees in the stand, which may be 
supplemented by a classification of crowns to indicate those now domi- 
nant, intermediate or already suppressed, and by a tabulation of past 
growth in diameter, by diameter classes (§ 278). The elements of 

436 



PREDICTION BASED ON GROWTH OF TREES 437 

uncertainty are probable loss of numbers in the next period, and future 
rate of diameter, height and volume growth of the survivors. At best, 
owing to the great difficulty of predicting for a given stand the loss in 
numbers and the rate at which diameter growth will be maintained, 
for long future periods, the method can be used only for periods of 
ten to twenty years, except for slow-growing or long-lived species where 
the factors of change are slowed down correspondingly. 

To apply this method of predicting tree growth to obtain current 
growth of stands, the steps are, 

1. Prepare a stand table of the forest or area (§ 188). 

2. As an aid in determining mortality, tally or estimate the number 
or per cent of each diameter class which is suppressed or will probably 
die within ten or twenty years. 

3. Decide upon the method to be applied in predicting diameter 
growth (§ 278 and § 279) and prepare table of growth by diameter 
classes to conform to the requirements of the method. 

4. Obtain data and construct a curve of average height growth 
(§ 248), which will probably be best expressed as current height growth 
based on height, for the last decade or two. 

5. Obtain volume tables giving the volume of trees of each diameter 
and average height. A standard volume table classified by heights is 
needed for best results. 

6. From present number of trees in each diameter class, deduct 
the per cent or number which will probably die within the period. 

7. Compute the average diameter which surviving trees of each 
diameter class will attain at end of period. 

8. Compute the increase in height for each diameter class. (The 
false method described in § 285 is frequently used as a substitute for 
a curve of height growth.) 

9. The volume of the present stand is calculated from the stand 
table and volume table. 

10. The volume of the surviving stand at end of period is obtained 
from the future diameter and height of the surviving trees of each diam- 
eter class, and volumes taken from the standard volume table. 

11. The difference in volume thus found is the net growth for 
the period, in stands which have not been thinned and in which no 
salvage of dying or dead timber is possible. The volume of the trees 
which die is thus deducted from the growth on the survivors, and 
only the net growth is represented in increased volume of the stand. 

In stands which are thinned, this prospective loss in numbers is 
not lost nor deducted, but is expressed in the form of thinnings. Where 
thinnings are marked and will be made in such stands, they will com- 
monly include more trees than will actually die during the period, 



438 CURRENT OR PERIODIC GROWTH OF STANDS 

since the suppression of diameter growth is to be avoided, and this begins 
considerably in advance of the death of the tree and may affect the 
entire stand if too crowded. 

By this method, neither a full volume analysis of current growth 
of trees is needed on the one hand, nor a yield table based on area and 
age on the other. Nor is it necessary to compute the average tree of 
the stand, and by predicting the growth of this tree for the next decade, 
seek to determine that of the stand ( § 275) since all the trees in the stand 
are given their proper weight in predicting growth. Only for very 
regular stands can average trees be used safely, and for such stands 
yield tables are better. 

337. Increased Growth of Stands after Cutting. The method of 
predicting diameter and volume growth of trees after release by cutting 
is shown in § 280. The problem of predicting growth of stands left 
on cut-over lands is one of properly combining the growth data for the 
different classes of trees left on the area. 

That diameter growth of individual trees should increase when 
their crowns and roots are given increased growing space is a natural 
law of growth of stands. The question is, " What is the total net 
current growth per acre on such lands? " 

The first result of cutting should be to tremendously increase the 
growth per cent on the remaining stand, or change its status, by removing 
large, old and slow-growing trees with a low growth per cent, and leaving 
small, young and more vigorous trees with a larger growth .per cent. 
This change would occur even if no increased growth followed the cutting. 

The total growth per acre laid on after cutting is the sum of the 
current increments on the residual trees. In spite of change in growth 
per cent or status, and of possible increased growth on the trees left, 
the total net volume increase may be less than on the original stand. 
If the number of trees is greatly reduced this is usually the case. But 
if the stand cut over is many-aged, and only the decadent and sup- 
pressed trees are taken, the combination of a large number of trees 
left on the area, an increased rate of growth on these trees, and especially 
the prevention, by cutting, of a loss of volume by death of trees which 
would otherwise have to be deducted from current growth, may result 
in a larger actual net increase per acre from the cut-over stand than 
before it was cut, as well as a greater growth per cent. 

This expansion of diameter and volume growth of the residual 
stand after cutting, is, for even-aged stands, a response to increased 
light, soil, moisture and space in which to expand. In many-aged 
stands it may mean, as well, an expansion of the total area of the age 
class (§ 253). 

The method of determining the growth of individual trees in the 



REDUCED GROWTH OF STANDS AFTER CUTTING 439 

stand to obtain the growth of the stand (§ 277), is favored in studies 
of cut-over lands, first, because such studies are usually made in many- 
aged stands of mixed species, second, because the difficulty of sepa- 
rating the age classes by area and age is even greater than on stands 
before cutting; hence the application to these stands of yield tables 
based on age is very difficult. 

The stimulation of growth on the trees left after logging is similar 
in character to the beneficial effects of repeated thinnings on stands 
under management. It undoubtedly increases the rate of jaeld per 
acre over that realized if the natural processes of selection are not 
interfered with. 

Two factors must be considered in analyzing this growth; first, 
to what extent have the trees left on the area been liberated or given 
increased growing space? — second, to what extent can they utilize or 
monopolize the area released by cutting? The maximum of increased 
growth would be found in a stand, either even- or many-aged, in which 
the cutting was so evenly distributed as to affect all of the remaining 
trees, and so light that the space released could all be absorbed by these 
trees. 

When cutting is either too light or too poorly distributed to affect 
all trees, the trees showing increased growth will be only a certain per 
cent of the total number. This per cent of each diameter class which 
will be released, as affected by the increased rate, will give the net 
actual increase over the previous rate of growth. 

Table LXVI illustrates the data required in a study of increased 
growth after cutting (p. 440). 

From a table of this character the average increase in growth may 
be computed by weighting the rate of increase by the per cent of trees 
affected; e.g., since 18 per cent of the trees are affected, an average 
increase of 18 per cent of the difference between the two classes of trees, 
those not affected and thus growing faster, can be added to the slower 
or original rate to get the new average for the forest. 

338. Reduced Growth of Stands after Cutting. In heavier cuttings, 
even on parts of the same cut-over area, openings may easily occur 
from cutting even-aged or mature groups, which affect but few of the 
remaining trees. These clear-cut spots will result in a net reduction 
of current increment per acre for the forest, just as would the clear 
cutting of a larger area. There is no possibility of increased growth 
because there is no timber left on which to lay this growth. In even- 
aged stands cut clear, the growth for the forest occurs on separate areas 
of maturing timber, not on the areas cut over; the growth on cut-over 
areas must result from reproduction of a new crop and come along in 
time. Thus on heavily cut-over areas, in mixed age classes, a heavy 



440 



CURRENT OR PERIODIC GROWTH OF STANDS 



reduction of growth per acre will occur for the present regardless of in- 
crease on the residual trees or stand. 

TABLE LXVI 

Adieondack Spruce 

Average Rate of Growth in Diameter on the Stump of 1593 Trees on Cut-over Land 
at Santa Clara, New York 



Diam- 
eter. 

Inches 


No. of 
trees 


Current 

annual 

growth in 

diameter 

just before 

first 

cutting. 

Inches 


Current 
annual 
growth in 
diameter 
since first 
cutting. 

Inches 


Current 

annual 
growth in 
diameter 
since first 

cuttmg. 

Values 

made 

regular by 

a curve. 

Inches 


No. of 
years 

required 

to grow 

1 inch 

in 

diameter 


No. of 

trees 

showing 

increased 

growth 


Current 
annual 
growth in 
diameter 
since first 
cutting. 

Inches 


5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 


8 

158 

329 

350 

277 

226 

135 

64 

30 

11 

1 

4 





095 
080 
090 
105 
120 
135 
130 
165 
165 
150 
080 
200 





095 
100 
110 
125 
140 
150 
145 
175 
170 
150 
080 
200 





09 

10 

109 

125 

140 

150 

160 

170 

178 

185 

192 

200 


11 

10 

9 

8 
7 
7 
7 
6 
6 
6 
6 
5 


1 

16 
63 

77 

59 

50 

18 

7 

2 

1 


0.100 
.180 
.185 
.205 
.205 
.215 
.210 
.240 
.170 
.200 


Average . 


0.112 


0.137 








0.20 








No. years to grow 
1 inch 


9 






7 




5 



Total number of trees, 1593. 

Number of trees showing increased growth, 294, or 18 per cent. 

The condition of such cut-over areas would be more accurately gaged 
if it were possible to separate the age classes in the cut-over stand on 
the basis of the actual area which they occupy. Thus, in a stand on 
which the timber cut formerly occupied 90 per cent of the growing 
space, it is not reasonable to expect that the trees which occupy the 
remaining 10 per cent of space will be able to expand sufficiently to 
absorb nine times their former crown space, even if properly distributed 



YIELD TABLES BASED ON AGE, TO CUT-OVER AREAS 441 

so as to make this possible. The increment on this area for any con- 
siderable period into the future depends on securing reproduction 
to fill the gaps. 

The method of measuring increment on cut-over lands solely by the 
growth expected on the trees left after cutting is best adapted to typical 
many-aged or "selection"^ forests, and the more closely the conditions 
both as to distribution of cutting and of the residual stand resemble 
a many-aged forest, the better the results obtained. This method 
gives best results also on areas under intensive management, where if 
trees die or are blown over, their volume is not lost, and when the danger 
of reduction or loss in numbers is at a minimum. 

The necessity for reducing the number of trees for loss during the 
period remains, and applies to all stands on cut-over lands as well as 
elsewhere. Neglect of this factor means over-estimation of probable 
net growth. 

339. Application of Yield Tables Based on Age, to Cut-over Areas. 
Where stands in the original forest can be or have been separated 
by area and age by any method, and a yield table based on age exists, 
a more conservative method of calculating growth on cut-over lands 
can be used, which bases this growth not on the theory of the many- 
aged forest and crown expansion of the age class, but on that of even- 
aged stands (§ 298). If age classes are on separate areas and cut clean, 
the cutting of one stand has no effect on the growth of another. If 
the forest is divided into age classes, and part is cut over, it can be 
assumed that this cutting removes an age class without stimulating 
the growth on the remainder, and that this area cut over is to be repro- 
duced to young timber rather than absorbed by existing age classes. 

To determine the area which is cut over, and that which remains 
stocked, the density or reduction per cent already determined for the 
original forest (§ 317) is assumed to apply to the residual stand. The 
area stocked to this degree of density can be found by dividing the 
volume in each age class left on the cut-over area, hy that of the empirical 
yield table for the given age which has been prepared for the original 
forest previous to cutting (§ 304). The sum of these areas, including 
that stocked already by young or immature age classes, subtracted 
from the total area, gives the area actually cut over. The actual yields 
of the age classes left on the cutover area will be in proportion to the 
per cent of the total area which they occupy, plus the degree of expansion 
or increased growth which they put on. The growth to be expected 
in the absence of any such expansion will be predicted by the empirical 
yield table from the net area or per cent of area stocked. This fixes 

1 Selection — A term applied to forests in which the entire series of age classes is 
intermingled over the whole area and not separated by areas. 



442 



CURRENT OR PERIODIC GROWTH OF STANDS 



the minimum expectancy and is safe for a long future period (§ 248). 
Studies of growth on the individual trees and on permanent sample 
plots as stimulated by release will in time indicate the maximum growth 
possible on the same area. The actual growth will be somewhere 
between these two extremes, dependent on the balance between the 

forces tending to expand the crown 
area, and the destructive agencies 
tending to reduce the numbers in the 
stand, as shown in Fig. 87 by the lines; 

A. Based on average growth per 
acre in original stand, with normal 
',oss of numbers. 

B. Based on increased growth after 
cutting and no loss of numbers. 

C. Probable rate somewhere between 
A and B, based on increased growth 
of a part of the stand and a reduced 
rate of loss in numbers. 

Probably the safest basis for growth 
prediction for long periods on cut- 
over lands is not the current growth 
study based on diameters, but, where 
possible, yields based on age, at the 
rate produced in the past on virgin 
forests, and figured for the net areas 
stocked, to which a percentage of in- 
crease may be added to represent expansion of crowns due to release 
and stimulus following cutting. 

An illustration of this principle of growth prediction is as follows: 

The empirical yield table for Western yellow pine, Coconino National Forest, 
Arizona, gives 66.2 per cent of the normal or index yield. 

The stand of timber left on the cut-over areas, separated into three age classes 
by the method given in § 321 is fovmd. 

By dividing the stand for each age class by the yield per acre from the empirical 
3aeld table, the area which is stocked with timber, for each age class, is determined. 

The area reproduced to poles and saplings is estimated. The total area of cut- 
over land is known. The remaining area, not shown as stocked either with mature 
timber or young timber is the area cut clean and awaiting restocking. The results 
are given in Table LXVII. 

The prediction of growth is now made by applying the empirical 
yield table to the areas and ages represented in the table. 

With the area and age of each age class indicated, the future yields 
on cut-over lands may be predicted by applying the empirical yield 
table, increased by the per cent of expansion agreed upon. 




Fig. 



87.— Possibilities of Growth 
on Cut-over Areas. 



PLOTS FOR MEASUREMENT OF CURRENT GROWTH 443 



TABLE LXVII 
Areas Remaining Stocked on Cut-over Lands 



Class 


Age. 
Years 


Yield per 
acre. 

Board feet 


Stand, 
total M. 

Board feet 


Empirical 

area 
equivalent 

acres 


Per cent of 

70,654 acres; 

also per cent 

of 1 acre 


Veteran 

Mature 

Blackjack 

Poles 


300 

200 

100 

50 

20 




12,050 

16,750 

7,480 

Totals .... 


27,900 

9,702 

70,908 




2,315 

579 

9,493 

6,006 

17,663 

34,598 


3.2 

0.8 

13.4 

8 5 


Saplings 

Not restocked. . . 


25.0 
49.1 




108,510 70,654 


100.0 



340. Permanent Sample Plots for Measurement of Current Growth. 

The best method of measuring the current growth of a stand is by means 
of permanent sample plots, established in stands which are typical of 
the conditions to be studied, and re-measured at intervals of from five 
to ten years. Methods of establishing and measuring such plots are 
described in § 243. In this way, just as for yield tables the actual net 
results of all factors which affect the current growth of the stand as a 
whole, such as wind, insects, disease, suppression, or increased growth, 
are measured, rather than either compared or predicted. The only 
precautions to observe on re-measurement of plots are that the diameters 
and heights of the trees must be taken in successive measurements in 
such a way as to give exact comparisons, whose difference indicates 
growth rather than discrepancies in re-measurements. 

Krauch has pointed out that the height of trees should be measured 
on such plots from the same position or point at each measurement, 
to avoid discrepancy due to the departure of the tree from the per- 
pendicular (§ 199). The diameter tape insures consistency in re-measure- 
ment of diameters (§ 190). The same volume table should be used in 
calculating successive volumes for trees of each size class. These pre- 
cautions insure the isolation of the current growth in successive measure- 
ments. 

341. Measurement of Increment of Immature Stands as Part of 
the Total Increment of a Forest or Period. The increment of a forest 
or large area, just as in the case of a single stand, may be expressed as 
the total growth over a definite period, or yield, the average annual 
growth or mean for this period, or the actual volume laid on each year 



444 CURRENT OR PERIODIC GROWTH OF STANDS 

or current annual growth. A forest resembles more closely a many- 
aged stand than one composed of a single age class. In such a stand 
or forest, it is not possible to separate one period which coincides with 
the complete cycle of production for a crop of timber, as can be done 
in the even-aged stand. The total production of the many-aged area 
or of the forest, for a period equal to that required to grow one crop 
from seed to maturity, may equal that of the even-aged stand, but it 
is laid on in many stands. 

In a regular many-aged forest the current growth for one year is 
the growth in volume of each stand, including those which are as yet 
unmerchantable. This is true of the forest, whatever its form. The 
current growth on the mature timber is but part of the total; that which 
represents the younger stands is equally important. Growth is not 
usually measured, on either trees or stands, until a size is attained which 
is merchantable for some form of product. Another reason for post- 
poning the measurement of young stands is that a very large per cent 
of the existing trees in such stands will never reach maturity, and the 
total volume at any period previous to an age at which it can be used 
is misleading and serves no useful purpose, while by contrast the natural 
selection of surviving trees in stands measured at merchantable age 
has already occurred and the results are accurately gaged. 

When the volume is finally measured on a young stand for the first 
time, it represents the growth for the entire preceding period. Perhaps 
but 10 per cent of the trees are large enough to measure at this time. 
After another decade, the stand is again measured. By this time 
50 per cent of the trees may be merchantable. The growth for this 
decade now includes the current growth, for ten years, on the original 
10 per cent, plus the growth since germination on the remaining 40 
per cent. At the third measurement, all trees which survive may be 
merchantable and are measured, but a portion of them have entered 
the merchantable class after being missed for the two previous decades. 
What happens is that although current increment by decades is sought, 
yet for trees which mature and are measured for the first time, total 
growth is substituted for current growth since there is no other way 
to handle it. 

If this example is now applied to a forest composed of a series of 
even-aged stands, the same thing is seen to occur. For the forest, 
the current increment is the increase in merchantable cubic volume 
of stands already partly merchantable; but to this is added, in each 
decade, stands measured for the first time, whose volume though added 
as current increment is in reality the total growth of several periods 
instead of one. It follows that for a stand just becoming merchantable, 
the apparent current growth will be very rapid during this process 



VALUE OF CURRENT GROWTH VERSUS YIELD TABLES 445 

while its actual average or mean annual growth, which takes in the true 
period required, is much less. 

But in a many-aged stand, or on a forest composed of stands of all 
ages, these elements counterbalance each other. As growth cannot 
be measured on stands below merchantable age or size, it is not meas- 
ured on "the areas covered by such young stands, or on the portion 
occupied by immature trees in mixed stands. But as soon as these 
stands or trees mature, the growth is measured all at once and greatly 
exceeds the actual current rate on the areas measured or for the trees 
in these age classes. Whenever the age classes are distributed evenly, 
the excess of current growth so caused is balanced for the area or forest 
by the neglect of the current growth on the younger stands. It follows, 
first, that in forests with well distributed age classes, the total current 
annual growth actually laid on in stands of all ages should be about 
equal to the current growth obtained by measuring only the merchant- 
able stands, provided the maturing volumes of young timber are included 
as current growth. For a single even-aged stand, or a forest devoid 
of younger age classes, this premise does not hold good, and the current 
growth for the period of early maturity will greatly exceed the real 
rate for the area or total period. On such stands or forests this rate 
will not be maintained, and the true yield must be found by dividing 
by age, in the form of mean annual growth. 

342. Comparative Value of Current Growth versus Yield Tables 
and Mean Annual Growth. The relative value and utility of the 
methods of studying the increment on forests or large areas may be 
summed up as follows: 

Increment or growth is always desired for areas of land rather than 
individual trees. 

The rate of growth per year on an average acre is the object sought. 

Where forestry is a permanent land policy, the rate of growth desired 
is that which represents the average for the life of a crop of timber, 
and which can be maintained, in consequence, indefinitely. 

This rate can be found most accurately whenever growth can be 
measured directly on the basis of area and total age, as in yield tables 
for even-aged stands, and applied to the forest by the necessary reduc- 
tion per cents. 

The current growth on stands or forests is best obtained from these 
same yield tables. 

But where it is not possible or practicable to construct such yield 
tables, current growth for short periods only can be measured directly 
on merchantable trees, and applied in predicting growth of the stand 
and forest. 

This method gains in accuracy over yield tables, by measuring 



446 CURRENT OR PERIODIC GROWTH OF STANDS 

directly the density of the stand, and by predicting growth on basis 
of actual volume and. conditions. It loses in comparison, because it 
measures only one current section of the growth curve for the stand or 
forest, which may be above or below the mean, and because the basis, 
the individual tree, while accurate to start with, rapidly loses its reli- 
ability, while by contrast, yield tables retain a fair degree of reliability 
over long future periods. 

Current growth, if it is actually measured in terms of volume, and 
the errors of using growth per cent are avoided, is well adapted to answer 
questions regarding the immediate future growth of specific stands, 
but is poorly adapted to growth predictions covering long periods. 

References 

Growth Rate in Selection Forest. Der Gemischte Buchen Plenterwald auf Muschel- 

kalk in Thiiringen, Mathes, Allgemeine Forst- u. Jagdzeitung, May 1910, p. 

149. Review, Forestry Quarterly, Vol. IX, 1911. p. 129. 
Increment in Selection Forests. Zur Ermittlung des laufenden Zuwachses speziell 

im Plenterwalde, Christen, Schweizerische Zeitschrift fiir Forstwesen, Feb. 

1909, p. 37. Review, Forestry Quarterly, Vol. VII, 1909, p. 206. 
A Method of Investigating Yields per Acre in Many-aged Stands, H. H. Chapman, 

Forestry Quarterly, Vol. X, 1912, p. 458. 
Accelerated Growth of Spruce after Cutting, in the Adirondacks, John Bentley, 

Jr., Journal of Forestry, Vol. XV, 1917, p. 896. 
Method of Regulating the Yield in Selection Forests, Walter J. Morrill, Forestry 

Quarterly, Vol. XI, 1913, p. 21. 
Determination of Stocking in Uneven-aged Stands, W. W. Ashe, Proc. Soc. Am. 

Foresters, Vol. IX, 1914, p. 204. 
The Relation of Crown Space to the Volume of Present and Future Stands of Western 

Yellow Pine, George A. Bright, Forestry Quarterly, Vol. XII, 1914, p. 330. 
Remeasurement of Permanent Sample Plots, G. A. Pearson, Forestry Quarterly, 

Vol. XIII, 1915, p. 60. 
Observations in Connection with Annual Increment of Growing Crops of Timber, 

Transactions of Royal Scottish Arboricultural Society, July, 1918, p. 164. 



CHAPTER XXXII 

COORDINATION OF FOREST SURVEY WITH GROWTH DETER- 
MINATION FOR THE FOREST 

343. Factors Determining Total Growth oil a Large Area. The 

solution of the problem of determining the amount or volume of wood 
which will be grown on a forest or area of forest land in a given period 
depends upon six factors: 

1. An analysis or classification of the forest into the areas included 
in each of the site quaUties present. 

2. The areas occupied by stands of given type and mixture of species. 

3. The actual present density of stocking, volume and number of 
trees, per acre, and size of diameters of the present stand on the forest. 

4. The actual age classes present, and the area which each occupies. 

5. The length of the period for which growth is desired, whether 
for a short current period, or for permanent management and a rotation. 

6. The rate of growth, to be determined by whatever method can 
best be applied to the forest as a whole by obtaining the actual growth 
on the stands which compose it. 

344. Data Required from the Forest Survey. The first four of 
these elements require the collection of data in connection with the 
forest survey. Studies of the rate of growth (6) for the period deter- 
mined (5) will not solve this problem in the absence of quantitative 
data to tie this growth study to the tract in question. 

Unless a forest is to be cleared for farms, the prediction of future 
growth is a basic consideration of its future management. A forest 
survey that is so conducted as to fail to obtain the necessary data on 
which growth for the forest can be determined must later be repeated 
to obtain this data, or supplemented in some way, while if the need 
were recognized at the start, the information could be obtained in final 
form with trivial extra cost. 

The character of this data depends upon the form of the forest as 
to its age classes. It may be itemized as, 

1. Site classification. 

2. Age of stands. 

3. Area of stands. 

4. Volume of stands. 

447 



448 COORDINATION OF FOREST SURVEY 

When these factors cannot be directly ascertained, the requisite basis 
must be obtained for calculating them. The most fundamental and 
useful basis is, 

5. Diameter of trees in stand by species, or a stand tal)le. 
Finally, because of its inadequate handling, special emphasis must 

be placed on obtaining 

6. The area stocked by immature age classes. 

345. Site Qualities — Separation in Field. Site qualities in the 
forest should be separated by area. Where several types exist, such 
as cove, lower slope, upper slope and ridge, which correspond closely 
with difference in site, the division by types goes a long way toward 
separating the site qualities (§ 228). 

Where site qualities must be determined directly, there are but two 
methods possible of which the first is direct judgment based on obser- 
vation of site factors, such as soil, altitude, slope, rock, moisture (as 
swamps) and general character of the timber growth. This niethod 
is subject to serious errors (§ 226). The second method ^ is ba.sed on 
the height growth of dominant trees (§ 227). But to determine directly 
the site class indicated by trees of different heights, their age must be 
known. When the forest is composed of a few laige age classes of even 
age, direct determination of a few ages may give this basis. 

But where the age classes are mixed, the age of individual dominant 
trees, rather than age of stand, must be relied on to indicate site quality. 
If we could assume that diameter growth did not decrease for the average 
tree, on poor sites, and that average trees of a given diameter were 
as old on Quality I site as on Quality III, diameter could be substituted 
for age; but average diameter growth varies with the site quality itself, 
which prevents this substitution. 

To obtain the basis of field classification of site, the heights of dif- 
ferent trees based on age are plotted and divided into site qualities 
based on the standard chosen, as illustrated in Fig. 84 (§310) except 
that in this case the data are obtained by plotting individual trees, 
and by analysis of the height growth of trees, rather than from plots. 

To apply this table or set of curves, in determining the quality of 
a given site, a selected tree or two is measured for height. If fully 
matured, total height may indicate directly the site quality. If the 
stand is young, age must always be ascertained. The average height 
for the given age is then looked up on the chart. The trees chosen 
should preferably be dominant and must never be suppressed. The 
position of the height with reference to the curves or table indicates 
the site quality. 

The unit of area on which sites are separated should be that used 
1 Journal of Forestry, Vol. XV, 1917, p. 552. 



RELATION BETWEEN VOLUME AND AGE OF STANDS 449 

in separating stands or units of volume estimating, such as small legal 
subdivisions, e.g., 10 acres, except where, by the aid of topography, 
the site qualities can be mapped to conform more closely with natural 
boundaries. Types are commonly separated in the forest survey by 
mapping the areas, and the estimate is usually separated to coincide 
with the divisions thus made (§221) though on forties this is not always 
done. 

346. Relation between Volume and Age of Stands. Density of 
stocking, as shown, is not determined by the total merchantable volume 
of a stand, but by a comparison of the existing volume with the index 
volume which stands should have at given ages. Density when deter- 
mined by comparison of volumes, is therefore a function not solely of 
area but also of age. To determine density for large areas, therefore, 
a basis of separation of the volume into age classes is required. This 
means either the direct mapping of areas of separate age classes, or a 
tally of diameters and a stand table for diameter classes in the stand. 
Methods of forest survey which utilize diameter tallies to obtain volumes 
(§ 207 and § 209) naturally lend themselves to the securing of such 
a stand table. The use of such tallies for determining age groups and 
average ages are shown in § 320 and § 323. In general, density of stock- 
ing for mature age classes will be found not in the field, but after the 
volumes have been computed or stand tables prepared, and by means 
of a comparison of volumes with the yield table, on the basis of similar 
ages. 

Age classes and their actual ages may be determined directly during 
timber survey only when the areas which they occupy are separate, large 
and eassily distinguished, and when time permits of the testing of trees 
for age. In intensive management, this method will l^e followed on small 
areas; but for large areas of mixed ages, the general method of depending 
upon diameters to indicate age should be relied on; hence the stand 
table is the basis of this age class division, both for age and area (§318 
to § 323.) 

347. Averaging the Site Quality for the Entire Area. Site qualities, 
when not correlated with type, present difficulties in classification, 
so much so that on large extensive projects site qualities may for the 
time have to be waived and an average yield table obtained for all 
sites. (This method was adopted in the preliminary working plan 
for the Coconino Nations' Forest, Arizona.) A composite stand table, 
including stands on all sites, is best for this purpose. Its application 
to the average site will depend on the average density or reduction 
per cent found for the area. Only when the divisions of the total area 
into site qualities can be coordinated with similar divisions of the esti- 
mate and stand can these divisions be made the basis of separate growth 



450 COORDINATION OF FOREST SURVEY 

predictions for the forest. Wherever possible, this division must be 
made. 

348. Growth on Areas of Immature Timber. The growth on any 
large area, whether the form of forest is even-aged in pure stands, or 
many-aged in mixed stands (§ 314) must include that of the young, 
unmerchantable stands. This growth is a prediction of future volume, 
and as such, may be obtained, not by measuring the present volume 
of the stand, nor by counting the number of trees in very young stands, 
but by the method of comparison with older stands. The yield table 
based on area and age gives this comparison. But to utilize the table, 
the one thing necessary to determine is the area which is stocked with 
the immature timber. Its age is more easily determined than for old 
timber, either by cutting or by counting whorls. Based on area and 
age, the future yield is a matter of density of stocking. The rate of 
growth per year may be taken as the mean annual growth, shown 
by the reduced or empirical yield table, for the age at which the stand 
will be cut. 

The density per cent for young stands is practically independent 
of the density of crown cover, and depends instead upon the number 
of trees per acre as compared with the normal number required at 
maturity, the distribution of these trees over the area, and the chance 
of survival (§ 316). Mortality in scattered stands where each tree 
has room to grow is much less than in crowded stands; and if the 
spacing of the reproduction is such that, allowing for a reasonable 
rate of loss from insects and causes other than suppression, the stand 
will reach full stocking at least a decade before maturity, it can be 
considered as fully stocked now. 

If a large area is being measured and an average density per cent 
is found for this area, resulting in an empirical jdeld table somewhat 
lower in values than the normal table, a conservative plan is to assume 
that the ultimate yield of young stands will not exceed this density, 
and to use the empirical yield table as the basis for calculating their 
future yields. 

That area and yield per acre is the only possible basis of prediction 
of yield for immature stands must become evident by considering the 
difficulties of the opposite plan, that of counting numbers of trees on 
snail plots. In tallying or counting reproduction or immature sizes, 
it is customary to lay off the plots at fixed intervals, comprising from 
one-tenth of the estimated strip, down to less than 1 per cent of the 
strip, and to count the seedlings and saplings upon these plots. The 
only way in which these data can be used to predict growth on such 
small timber is by predicting the percentage of this count which will 
survive. The mjethod of comparison by numbers of trees is useless, 



GROWTH ON AREAS OF IMMATURE TIMBER 451 

first, because number of trees per acre at these ages does not in any way 
indicate the future yield, since this is determined by the number that 
survive; second, because the area rather tlian the number will determine 
the future yield. On a plot of 100 square feet there may be one hundred 
seedlings; yet if fully stocked at maturity not more than one tree would 
be able to survive from this number. Such counts on plots serve only 
to determine the extent to which reproduction is becoming established 
and do not give the data needed for growth predictions. 

Age Classes Based on Size. Immature timber may be divided into 
at least three classes for purposes of growth study; seedlings, saplings 
and poles. Seedlings are trees under 3 feet high.^ Saplings include 
trees from 3 feet high to 4 inches D.B.H. Poles are trees from 4 to 12 
inches D.B.H. 

Saplings may be divided into 
Small — from 3 to 10 feet high. 
Large — from 10 feet high to 4 inches D.B.H. 

Poles may be divided into 

Small — from 4 to 8 inches D.B.H. 
Large — from 8 to 12 inches D.B.H. 

Methods for Seedlings and Saplings. In determining the quantity 
of reproduction and immature timber present on an area, in order to 
predict its growth by comparison with a yield table, the procedure 
will depend upon the form of the forest. In even-aged stands, areas 
stocked with seedlings in sufficient numbers can be entered by mapping 
them as fully stocked. Danger of destruction is chiefly by fire, and for 
this, correction can be made when fires occur. But in many-aged 
stands, suppression must be considered. Depending upon the silvical 
characteristics of the species and the behavior of the seedlings, the object 
should be to record only the area of mature forest which will result from 
the present stocking. Seedlings which are suppressed will be ignored. 
Those which grow in openings and are thrifty wiU be regarded as prob- 
able survivors. In rather open, group-selection - forests like yellow 
pine, the areas stocked in this manner are easily distinguished. With 
species such as spruce, seedlings starting under shade and not in open- 
ings should be disregarded altogether, both because of suppression, 
and because their age will be prolonged by this cause and they will 
not become an economic factor in the stand till a later period (§ 263). 

With saplings, the establishment of the stand in many-aged forests 

1 Standard definitions, Society of American Foresters. 

^ Group-selection, a forest composed of trees of all ages intermingled in small 
fairly even-aged groups. 



452 COORDINATION OF FOREST SURVEY 

is more certain, and the area so stocked with trees which will probably 
survive can be better determined. 

For both these classes of timber, the best method of determining the 
area, and consequent future growth, during the forest survey, is to record 
on each strip the per cent of total area on the strip which is stocked 
with young timber, on the basis of probable survival to maturity. 
This per cent is then reduced to acres for the strip. The average size 
and age can also be noted. Seedlings and saplings can be separately 
noted, or thrown together, depending on the intensiveness of the work 
and size of area. 

A second method of record on the basis of area, formerly used in the 
Southwest, was to note the reproduction in general terms, based on 
whether the stocking was sufficient to replace the present stand. If so 
it was termed excellent. Different per cents less than this were termed 
good, fair, poor, and none. This system does not distinguish between 
the areas of mature and young timber or consider the relation which 
one bears to the other. 

To supplement the per cent method of ocular guessing at areas 
restocked, plots may be laid out at given intervals, on which the areas 
stocked can be mapped, and computed in terms of acres. The per cent 
of the plot thus shown as reproduced serves to correct the ocular work 
and to check the results. 

Methods for Poles. With poles, the area method can still be applied 
directly in even-aged stands, by mapping. In many-aged stands, a 
choice of two methods is offered. Either the area per cent can be used 
as for saplings, but separately, and the number of trees in this class 
ignored as before, in which case merely the average size and age of the 
poles on each strip is recorded with the per cent of area occupied, or 
instead, the poles may be counted. 

The purpose of the count is to obtain a second basis of comparison 
with the empirical yield table. The latter should show the number 
of trees per acre required at different ages. The yield table data may 
be made to include pole sizes, by including plots of this age in construct- 
ing the normal tables of yield. In case this has been done, the area 
occupied by poles can be very roughly determined by means of the 
numerical comparison with the empirical table. For instance, if poles, 
averaging sixty years old and 7 inches in diameter run 120 per acre 
in the normal table, and the reduction per cent is 66|, the empirical 
stocking is 80 poles per acre. A count of 8000 poles on the area indicates 
an area of 100 acres stocked with pole sizes. 

A definite plan for the determination of the stocking with poles must 
be made preliminary to undertaking the timber survey. Trees which 
are part of an even-aged mature stand, but which are not yet merchant- 



SEPARATION OF AREAS OF IMMATURE TIMBER 453 

able or are suppressed, are not considered, since the yield table for the 
stand takes care of them. Only in many-aged stands must poles be 
counted, or their area determined by per cent of the total, the former 
method to be used if the yield table permits of direct comparison of 
numbers, the later, if only the mature classes are shown in the table. 

349. Efifect of Separation of Areas of Immature Timber on the 
Density Factor for Mature Stands. The separation by area of the 
immature age classes accomplishes more than the determination of 
future jaeld for these age classes. In the many-aged forest, the mature 
timber is not segregated as it is in even-aged stands, but is intermingled 
with areas of reproduction, saplings, and poles. In the attempt to 
separate this mature timber into two or more age classes, either based 
on diameter classes, or by age groups (§ 320 and § 323) it is necessary to 
begin with a knowledge of the total area occupied by all the mature 
age classes. If the area actually stocked with seedlings, saplings and 
poles to the exclusion of mature timber is neglected, then the area appar- 
ently required by the mature timber is greater than that actually 
required, by just the amount of this error. In the even-aged forest 
no such mistake is possible, and by analogy, its correction for the many- 
aged forest must be undertaken. 

The effect of not separating the area of immature stands is to lower 
the reduction per cent or apparent density factor for the mature age 
class. E.g., a reduction per cent of 40 is found for mature timber when 
it is assumed to occupy the entire area. Segregation of young timber 
shows that one-half or 50 per cent of the area is occupied by these age 
classes. The total area is 10,000 acres. The actual area occupied by 
mature timber is now 5000 acres, which doubles its density, and gives 
a density per cent of 80 instead of 40. 

At first glance it would appear that no difference is made in the cal- 
culation of yield of these mature age classes by either assumption since 
reduced area and increased density are reciprocal and refer to the same 
actual stocking and volume and presumably the same future yield. 
The benefit lies in the fact that the corrected density factor more nearly 
indicates the rate of growth per year for the forest or on the average acre, 
which is the information most needed in permanent management. 
By separating the yield and area of the young timber, it is possible 
to predict the total actual yield of the forest over a long period, instead 
of for the shorter period required to harvest timber now mature. Instead 
of an extremely low per cent of density for mature timber and for the 
forest, which would indicate the need of considerable reduction in yields 
from the standard table (§ 316), the true conditions are revealed. 
Finally, it gives the same data as to age classes for the many-aged 
forests as are obtained by mapping for even-aged stands. 



454 COORDINATION OF FOREST SURVEY 

350. Stand Table by Diameters for Poles and Saplings: When 
Required. When diameter is definitely substituted for age and area, 
the growth of the forest for a period of from ten to twenty years into 
the future will include not only the increase on existing merchantable 
trees, but the volume of all young trees which grow during the period 
to a size which brings them into the merchantable class (§ 277). 

The number of diameter classes which will become merchantable 
will be determined by the length of the period and the rate of growth 
in diameter. At a rate of 1 inch in five years, trees now 4 inches below 
the minimum diameter will reach the required size in 20 years. 

In order to predict the growth of the stand for this period, the number 
of trees of each diameter class included in the group which will mature 
within the period must be recorded during the forest survey. Either 
all of the trees of these sizes must be calipered or counted, and the 
average diameter approximated, or these sizes may be calipered on a 
part of the area, distributed mechanically to obtain an average for the 
whole. This again indicates the need for correlation of the method 
to be used in predicting growth with the timber survey, before the latter 
is undertaken. 

References 

Coordination of Growth Studies, Reconnaissance and Regulation of Yield on National 
Forests, H. H. Chapman, Proc. Soc. Am. Foresters, Vol. VIII, 1913, p. 317. 



APPENDIX A 
A. LUMBER GRADES AND LOG GRADES 

351. Purpose of Log Grades. The most useful purpose of timber estimating 
and log scaling is to determine the value of the bgs and standing timber. This 
value depends upon the amount or per cent of lumber of different qualities which 
can be obtained from the logs or timber to be valued. In § 87 it was shown that for 
this purpose logs are separated into grades, usually three m number, but that the 
specifications for and value of each log grade depend upon the contents of logs as 
expressed in grades of lumber, and in resultant average value or price per 1000 board 
feet. 

352. Grades of Lumber. Wood varies in texture or closeness of grain, difference 
between heart- and sapwood, uniformity of texture and freedom from knots, number, 
size, placement and character of knots, and presence of or freedom from various 
defects which lower the value of the piece by altering its appearance, strength, 
surface or suitability for the purposes for which it may be used. Pieces which are 
entirely free from all defects are suitable for the highest uses and possess the greatest 
value. At the opposite extreme are found pieces with defects so numerous or serious 
that they are unfitted for any useful purpose, hence possess no market value and are 
disposed of as refuse to the burner or as fuel. Certain " cull " grades, formerly 
refuse, are now generally handled as merchantable, but the practice of scaling has 
not been altered and such grades are still excluded from the scale as unsound. 

The output of a mill in lumber, if separated according to the quality and value 
of each board, would form an unbroken series from the most perfect pieces descend- 
ing through an increasing per cent of more and more serious defects until the poorest 
merchantable boards are passed, and refuse only is left. 

For practical purposes, this series must be separated by arbitrary standards 
into groups termed lumber grades, so defined that any piece may be assigned by its 
appearance to its proper classification or grade. These grades are then made the 
basis of lumber prices and lumber trade. 

The specifications for a grade are intended to defuie the poorest piece which will 
be accepted in the grade, thus excluding all lumber whose quality and defects are 
such as to unfit it for this grade. The average quality of lumber in any grade will 
therefore be better than the minimum specifications. Lumber which would qualify 
for a given grade is sometimes included in a lower grade, but this is not in the interest 
of the seller and tends to destroy the standards of grading. 

353. Basis of Lumber Grades. The requirements of a lumber grade are, that it 
be generally adopted in a region or for the trade which handles the lumber from this 
species or region; that it be consistently applied throughout this region; that it be 
capable of definition and application in grading; and that it conform to the require- 
ments for certain definite uses of lumber. To use lumber for a given purpose, when 
it is better than is necessary and is suitable for a higher use, is wasteful, but to admit 

455 



456 APPENDIX A 

lumber to a grade intended for a given use, when it possesses defects which unfit it 
for this use, destroys the basis of sound business. 

Again, a grade, as apphed to the lumber of a given species or region, must be so 
defined as to permit of securing a sufficient volume of output qualifying for the 
grade to make it a commercial or market product. No purpose is served in making 
grades for clear lumber, to apply to second-growth stands which produce little if any 
lumber of this grade. 

Defects characteristic of one species but absent or rare in others call for modi- 
fications of grading rules to suit the species in order to prevent the rejection of too 
large a percentage of the output for grades for which it is otherwise suited. 

To secure uniformity in both definition and application, grades of lumber are 
established by regional associations of lumber manufacturers and dealers, which 
frequently employ a corps of grading inspectors acting under a central head. These 
grading rules are modified from time to time as market conditions change. The 
latest specifications for any region or species should be obtained from the local 
associations. Not only do specifications change, but there is considerable fluctua- 
tion in their application as a whole, and in individual mills, which it is the purpose 
of inspection and standardization to avoid as far as possible. 

354. Grades for Remanufactured and Finished versus Rough Lumber. For 
the }niri)ose of valuing logs and standing timber, only those grades of lumber are 
serviceable which can be applied with some degree of accuracy directly to the log. 
Lumber is finally sold on the basis of its grade when finished or remanufactured. 
But these final grades are made the basis of the grading of the rough boards on the 
sorting table, with the modification that the better grades of rough lumber may be 
split up into several special grades, including lumber intended for specific uses. In 
all such cases, the general grade of the rough lumber is the basis of log grading. 

Structural and dimension lumber calls for a difi'erent basis of grading, as do 
sawed cross ties. Where a considerable proportion of the output is in these forms, 
the basis of log grading is affected. While a system based on this form of products 
could be worked out for logs, it has not been attempted, but the basis of log grades 
has been confined to 1-inch rough lumber. The average value of each standard grade 
of lumber may be obtained from that of the gi'ades of remanufactured lumber which 
it produces. 

It is always possible to recognize and estimate separately the quantity and value 
of trees containing unusual or special dimensions, in the nature of piece products. 

355. General Factors which Serve to Distinguish Lumber Grades. Face. Lum- 
ber is graded on the appearance of the poorest face for certain uses and in certain 
regions. For other uses and in other regions, the appearance of the best face deter- 
mines the grade. The specific practice is in each case determined by the local grad- 
ing rules. 

Defects. With respect to perfect pieces, all departures from standard as defined 
in § 352 constitute defects. With regard to each specific grade, the defects which 
disqualify the piece and throw it into lower grade are defined. Defects which dis- 
qualify in one grade may be accepted in the grade below. 

The principal defects are caused by, 

1. Knots, sound or unsound, encased, firm or loose, and knot holes. 

2. Rot. 

3. Shake, season checks, seams and cracks. 

4. Pitch. 

5. Worm holes. 

6. Stain, either as blue sap or red heart. 



LUMBER GRADES AND LOG GRADES 457 

7. Mechanical defects, as splits, torn grain. 

8. Wane, or round edges. 

These defects or any combination of them may reduce grade by affecting the 
utility and value of the piece through its appearance, surface, texture, or strength. 

356. Grouping of Grades of Rough Lumber. Even when standard grades of rough 
lumber only are considered, it is best not to attempt to base log grades or quality of 
standing timber on the determination of given per cents of each of these standard 
grades supposed to be contained in the logs. Instead, these grades should be com- 
bined into a few groups with similar characteristics conforming to the grading rules 
for the species and region. Three such groups may be distinguished in softwoods, 
namely, finishing grades, factory or shop grades, and common grades. Based on the 
practice of " sound " scaling, a fourth group may be made to include grades which 
contain rot or other defects in sufficient quantity to cause their rejection in scaling 
logs. 

Finishing grades include all of the so-called upper grades of lumber, characterized 
by freedom from all but a few small defects. These grades are suitable for use with- 
out being cut up, for purposes requiring appearance as the prime factor, combined 
with definite and sometimes considerable width and length. 

These grades are used for outside and inside finish and for many purposes of 
manufacture. The entire piece is graded as a unit, any defect serving to reduce its 
grade as a whole. 

Factory or Shop Grades. Boards suitable for factory or shop grades are such as 
will yield smaller pieces of upper grade material when ripped or cut up as to exclude 
or cull out disqualifying defects. In these grades, therefore, the piece is not graded as 
a unit but on the basis of the per cent of its volume that can be utilized. The 
remainder is rejected as refuse and may therefore contain defects of any character 
without affecting the grade of the piece. 

Common Grades. As applied to lumber cut from conifers or " softwoods," com- 
mon lumber is distinguished from the other two groups by a general coarseness of 
appearance caused by various defects or combinations of defects, such as nu- 
merous large or small knots, which not only render it unsuitable for the ujiper grades 
but prevent cuttings being made from it which would qualify it for factory grades. 

Common lumber of this class is graded for the entire piece and finds its principal 
use in construction. Owing to the large volume of common lumber, in conifers, 
which constitutes from 60 to 95 per cent of the total output, this group may be 
subdivided in each given region. These specific common grades are not always 
given identical names any more than are the grades in the other two groups. The 
most widely accepted nomenclature is, 
No. 1 Common, 
No. 2 Common, 
No. 3 Common. 

357. Example of Grading Rulss. Southern Yelloio Pine. — Finishing, or Upper 
Grades. " A " Finishing, inch, IJ, I5 and 2-inch, dressed one or two sides, up to 
and including 12 inches in width, must show one face practically clear of all defects, 
except that it may have such wane as would dress off if surfaced four sides. 

13-inch and wider " A " finishing will admit two small defects or their equivalent. 

" B " Finishing, inch, Ij, I5 and 2-inch, dressed one or two sides, up to and 
including 10 inches in width, in addition to the equivalent of one split in end which 
should not exceed in length the width of the piece, will admit any two of the following 
or their equivalent of combined defects: slight t«rn grain, three pin knots, one 
standard knot, three small pitch pockets, one standard pitch pocket, one standard 



458 APPENDIX A 

pitch streak, 5 per cent of sap stain, or firm red heart; wane not to exceed 1 inch in 
width, J-inch in depth and I the length of the piece; small seasoning checks. 

11-inch and wider " B " Finishing will admit three of the above defects or their 
equivalent, but sap stain or firm red heart shall not exceed 10 per cent. 

Select Common Finishing, up to and including 10-inch in width will admit, in 
addition to the equivalent of one split in end which should not exceed in length the 
width of the piece, any two of the following, or their equivalent of combined defects: 
25 per cent of sap stain, 25 per cent firm red heart, two standard pitch streaks, 
medium torn grain in three places, slight shake, seasoning checks that do not show 
an opening through, two standard pitch pockets, six small pitch pockets, two stand- 
ard knots, six pin knots, wane 1 inch in width, ^ inch in depth and one-third the 
length of the piece. Defective dressing or slight skips in dressing will also be allowed 
that do not prevent its use as finish without waste. 

11 and r2-inch " C " Finishing will admit one additional defect or its equivalent. 
Pieces wider than 12 inches will admit two additional defects to those admitted in 
10-inch or their equivalent, except sap stain, which shall not be increased. 

Pieces otherwise as good as " B "' will admit of twenty pin-worm holes. 

Common Grades. No. 1 Common boards, dressed one or two sides, will admit 
any number of sound knots. The mean or average diameter of any one knot should 
not be more than 2 inches in stock 8 inches wide, nor more than 2§ inches in stock 
10 and 12 inches wide; two pith knots; the equivalent of one spht, not to exceed in 
length the width of the piece; torn grain, pitch, pitch pockets, slight shake, sap stain, 
seasoning checks, firm redheart; wane I inch deep on the edge not exceeding 1 inch 
in width and one-third the length of the piece, or its equivalent; and a limited num- 
ber of pin-worm holes well scattered; or defects equivalent to the above. 

No. 2 Common boards, dressed one or two sides; No. 2 Shijjlaii, Grooved Roof- 
ing, D. & M. and Barn Siding will admit knots not necessarily soimd; but the mean 
or average diameter of any one knot shall not be more than one-third of the cross 
section if located on the edge, and shall not be more than one-half of the cross section 
if located away from the edge; if sound may extend one-half the cross section if 
located on the edge, except that no knot, the mean or average diameter of which 
exceeds 4 inches should be admitted; worm holes, splits one-fourth the length of 
the piece, wane 2 inches wide or through heart shakes, one-half the length of the 
piece; through rotten streaks ^ inch wide one-fourth the length of the piece, or its 
equivalent of unsound red heart; or defects equivalent to the above. 

A knot hole 2 inches in diameter will be admitted, i)rovided the piece is otherwise 
as good as No. 1 Common. 

Miscut 1-inch common boards which do not fall below f-inch in thickness shall 
be admitted in No. 2 Common, provided the grade of such thin stock is otherwise 
as good as No. 1 Common. 

No. 3 Common boards, No. 3 Common Shiplap, D. & M. and Barn Siding is defect- 
ive lumber, and will admit of coarse knots, knot holes, very wormy pieces, red rot, 
and other defects that will not prevent its use as a whole for cheap sheathing, or 
which will cut 75 per cent of lumber as good as No. 2 Common. 

358. Relation between Grades of Lumber and Cull in Log Scaling. From the 
standpoint of the lumber trade, lumber which is merchantable, no matter what the 
extent and character of defects it contains, is placed in a recognized grade, while 
cull lumber is lumber which is not merchantable. Grades of common lumber below 
No. 3 are sawed from unsound or defective portions of logs, which would be culled 
in scaling. In mill-scale studies and in determining log grades, it is proper, there- 
fore, to throw all grades under No. 3 Common into the group termed cull. In addi- 



LUMBER (illADES AND LOG GRADES 459 

tion, the grade designated as No. 3 Common may in certain regions contain unsound 
material which would not be scaled on the basis of sound scale. Hence a portion of 
the No. 3 grade, if so constituted, plus all of the cull grades of lumber, when utilized, 
go to increase the amount of over-run secured in manufacture. 

From one to three grades of lumber below No. 3 Common may be recognized, 
according to the species and region. 

Common Grades Culled in Sound Scale of Logs. Southern Yelloiv Pine. No. 4 
Common boards shall include all pieces that fall below the grade of No. 3 Common, 
excluding such pieces as will not be held in place by nailing, after wasting one-fourth 
the length of the piece by cutting into two or three pieces ; mill inspection to be 
final. 

359. Log Grades. Determination. The purpose of defining log grades is to 
furnish a basis for separating the logs into groups whose average value or price per 
1000 board feet can be determined, instead of attempting to arrive at an average 
price for the entire run of logs. Three such groups permit of a sufficient differentia- 
tion for this purpose. 

Where logs are not bought or sold, but standing timber is manufactured by the 
purchaser, log grades (§87) form the best basis for appraising the value of this timber. 

The specification for determining the grade of logs must apjily to the external 
appearance and dimensions of the log. In application, logs on the border line between 
two grades are usually thrown to the grade below, since a part of the surface is invis- 
ible. Log grades are based on 

1. Minimum diameters and lengths. 

2. Surface appearance, and presence of knots or visible defects. 

3. Judgment of scaler, based on 1 and 2 as to the minimum per cent of upper 

or better grades of lumber contained therein. 

The specifications for log grades are more elastic than for lumber grades, since 
the presence of a small per cent of high grade lumber may serve to offset serious 
defects and give the log the value of a grade from which it would be excluded if based 
solely on quantity or scale. These specifications should be drawn in such a manner 
as to furnish the most serviceable basis of subdivision of the existing range of quality 
found for the species and region, which object may be secured by modifying the 
requirements as to size and per cent of upper grades required for logs of first and 
second grades. 

Log grades should be established only after thorough mill-scale studies, and by 
some agency similar to that of the United States Forest Service or a Lumber Manu- 
facturers' Association, so as to secure uniformity over as wide an area as possible. 

Within the limits of a log grade a certain variation in average quality will occur 
in different quantities of logs, owing to the preponderance of higher or lower grades 
of lumber within the limits set. The quality of the logs which form the basis of the 
mill-scale study may be better or poorer than the average, even after classification 
into grades. But as logs and timber stumpage are worth considerably less than 
lumber, it is unnecessary to attempt a greater refinement; nor could it be practically 
applied. 

Diameter For logs of the best grade, diameter is a reliable guide. Up to a 
certain size, trees retain the branches, either alive or dead, and the central bole of 
the tree is filled with these knots. Stunted, slow-growing, and consequently small 
trees still have these knots, and during their growth, have made very little clear 
lumber. Large trees, on the other hand, even if no older, have laid on much clear 
wood outside of the knots. 

The minimum diameter for the highest grade can be fixed to include jiractically 



460 APPENDIX A 

all logs of this class, not barred by knots or defects. This diameter will vary with 
the same species in different regions, and for different species. 

Effect of Defect upon Grades of Logs. The defect most easily seen, both in logs 
and standing timber, is a knot. In grading hardwood logs, one somid, bright knot, 
with a maximum diameter of 4 inches is taken as a standard defect. Other defects 
are compared with this knot, on the basis of an equal amount of damage to quality. 
These may be worm holes, smaller or larger knots, shake, rot, cat faces or fire scars. 
The maximum number of standard defects, or their equivalent, is prescribed for each 
grade of logs. 

For conifers, a different system is employed, and the specifications lay stress on 
the possible percentage of yield of certain grades, with indication as to the general 
appearance and character of defect in logs which will yield this ratio. 

Defects are of two classes, those which cause loss of grade, but no discount in 
total scale, i.e., sound defects, and those which require elimination from the scale 
of the defective part. To the first class belong sound knots, stain, firm red heart 
and pitch. In the second class fall rot, shake, fire scars, cat faces, and crook or 
sweep. Worm holes may be in either class, according to size and frequency. 

In the grading of hardwood logs, no distinction is made, and the presence of more 
than two " standard " defects serves to throw the log into the lowest class, or No. 
2, except when over 24 inches in diameter, when it must cut at least 75 per cent of 
No. 1 common and better lumber. 

With conifers, the presence of either class of defect will not reduce the grade of 
a log as long as the minimum percentage of upper grades can still be secured. But 
in reality, the value of the log is greatly lessened by such defects. With increasing 
amounts of defect, the log is de-graded cither to second or third grade, and finally 
is rejected as cull. 

360. Examples of Log Grades. Hardwoods — National Hardwood Lumber 
Association, 1916 Oak, White and Red. 

No. 1 logs. 2 inches of bright sap is no defect. Sap in excess of 2 inches is one 
standard defect. 

No. 1 logs must be 24 inches and over in diameter. 

24 to 29 inches inclusive will admit of one standard defect or its equivalent. 

30 inch and over will admit of two standard defects or their equivalent. 

Select. Select logs must be 18 inches and over in diameter. 

2 inches of bright sap is no defect. Sap in excess of 2 inches is one standard defect. 

18 to 21 inches wide inclusive must have ends and surface clear. 

22 and 23 inches will admit of one standard defect or its equivalent. 

24 inches and over will admit of one more standard defect than is admitted in No. 
1 logs of same size. 

No. 2 logs. No. 2 logs must be 16 inches and over in diameter. 

Bright sa]) is not a defect in this grade. 

16- and 17-inch will admit of one standard defect or its equivalent. 

18 to 23 inches inclusive will admit of two standard defects or their equivalent. 

24 inches and over must cut 75 per cent or more into No. 1 common and better 
lumber. 

The grades for other species arc similar. 

Softwoods — Columbia River Log Scaling and Grading Bureau, Washington 
and Oregon, 1920. 

No. 1 Logs. No. 1 logs shall be logs which, in the judgment of the scaler, will be 
suitable for the manufacture of lumber in the grades of No. 2 clear or better to an 
amount of not less than 50 per cent of the scaled contents. 



LUMBER GRADES AND LOG GRADES 461 

No. 1 logs shall contain not less than six annual rings to the inch in the outer 
portion of the log equal to one-half of the log content; and No. 1 logs shall be straight 
grained to the extent of a variation of not more than 2 inches to the lineal foot for a 
space of 2 lineal feet equidistant from each end of the log. 

Rings, rot, or any defect that may be eliminated in the scale, are permitted in a 
No. 1 log, providing their size and location do not prevent the log producing the 
required amount of No. 2 clear or better lumber. 

A No. 1 log may contain a few small knots or well scattered pitch pockets as per- 
mitted in grades of No. 2 clear or better lumber; or may contain a very few grade 
defects so located that they do not prevent the production of the required amount of 
clear lumber. 

No. 2 Logs. No. 2 logs shall be not less than 12 feet in length, having defects 
which prevent their grading No. 1, but which, in the judgment of the scaler, will 
be suitable for the manufacture of lumber, principally in the grades of No. 1 common 
or better. 

No. 3 Logs. No. 3 logs shall be not less than 12 feet in length, having defects 
which prevent their grading No. 2 but which, in the judgment of the scaler, will be 
suitable for the manufacture of inferior grades of lumber. 

Cull Logs. Cull logs shall be any logs which do not contain 335 per cent of sound 
lumber. 

Logs which contain considerable clear lumber but not sufficient to grade No. 1, 
and contain also large coarse knots or other grade defects of No. 3 quality, will be 
classed as No. 2 if the average value of the lumber falls in this class, regardless of its 
actual grade. Logs which are on the border line between two grades should be graded 
alternately or in equal amount in the upper and the lower grade. 

361. Mill-Grade or Mill-scale Studies. In §81 and §82 it was shown that the 
log scale should make no attempt to measure the actual sawed contents, which is 
the sum of the scale, plus this over-run. It is equally impossible for the scaler to 
separate his scale into grades, for in doing so he w^ould be compelled to substitute 
judgment for facts; yet the actual value of logs can be determined onl}' by a knowl- 
edge of both of these factors. 

When the sawed output of a run of logs has been tallied and totaled separately 
by grades, its comparison with the log scale shows for the entire qv.antity scaled, the 
average over-run per thousand board feet of scale, and the per cent represented by 
each grade produced. The value of the product of an average thousand feet B. M. 
log scale in terms of sawed lumber is determined by first multiplying the price of 
each grade of lumber sawed by the per cent of the grade in one thousand board feet, 
adding the by-products, and multiplying by the total per cent of over-run. 

This general check, applied to an average run of logs, and termed the mill run, 
will serve to determine the value of similar average sizes and quality. But for 
timber averaging larger or better, or smaller, knottier and poorer, the true value can 
be obtained, by this method, only after sawing. 

But individual logs of similar sizes possessing certain distinctive features, as 
shown by surface indications such as clearness, knots and other defects, will cut out 
about the same per cent of grades and values wherever found. 

By using the log as the standard, it is possible to apply the results of mill-scale 
studies of separate logs to stands whose average quality may be entirely different 
from that which is being sawed, provided only that some logs of all qualities are 
analyzed. For this reason, mill-scale studies should be based on the separate analy- 
sis of the product of individual logs, by grades of lumber. Such studies determine, 
for logs of each diameter, length and grade, first, the over-run in sound lumber, and 



462 APPENDIX A 

in all merchantable grades; second, the amount of each standard grade of rough 
boards, expressed in per cent of the total scale of the log, net and gross. 

362. Method of Conducting Mill-scale Studies. A tabulation, classification 
and summary of the logs so analyzed permits, first, a correlation between logs of given 
sizes, appearance and defects, and the actual sawed contents in grades which these 
logs will produce, hence their actual value; second, the adoption of arbitrary 
specifications for separating the logs themselves into log classes or grades; third, a 
comparison of the value of logs of each size and grade with the cost of logging them, 
enabling both owner of stumpage and operator to determine both the lower limits of 
merchantability as to minimum size and per cent of sound lumber in a log which 
warrants its removal and manufacture, and in case only a portion of the merchant- 
able stand is removed, to know the relative value and profit of removing certain 
definite classes and sizes of material and leaving others (§ 96). 

The steps in a mill-scale study are : 

1 . Decision as to the exact number and designation of the grades of rough lumber 
to be tallied. 

2. Scale and record of each log, on the deck. If log grades have already been 
adopted, the scaler assigns each log to its apparent grade. A full record would 
embrace the following items: number of log (serial); length, in feet and inches; 
position in tree, as butt, middle, top; species; average diameter inside bark at small 
end ; at large end ; width of sapwood ; thickness of bark ; scale, by standard log rule, 
full and net after deductions for cull defects; estimated log grade; description of 
defects, preferably graphic, on a diagram showing large and small ends, and both 
sides of logs. This record requires one man, an experienced log scaler, who will 
place a number on each log to coincide with his record. Logs scaled sound are given 
a special mark, and separated in the final tables. 

3. Identification of this product of separate logs. A marker standing behind the 
head saw marks with crayon each piece sawed from a log. The number of the log is 
placed on the first few pieces. Different-colored crayons are used for alternate logs. 
A count may be made of the total number of pieces from a log, as a check on the tally. 
This work is made quite difficult by a resaw, which tends to mix the products of con- 
secutive logs on the chains and requires the marking of both sides of the piece. Gang 
saws further complicate the study. The marker can also check logs scaled as sound 
for unseen defects appearing in sawing, and make final record of the logs which saw 
up sound. 

4. Record of grades and sizes. An expert grader, familiar with the standard for 
the species and locality, will grade each piece. The record, kept on a separate sheet 
for each log, and given the log number, will show length, width, and grade, by pieces, 
and a recapitulation or summary for the log, giving in addition to the data copied 
from the scales, the total board-foot contents in each grade, and the per cent of the 
sound scale which this equals. This tally requires the services of a tallyman, mak- 
ing a crew of four men. 

5. Additional data needed, (a) Data on per cent of total contents utilized 
embrace the measurement of the cubic contents of a log, and the analysis of the 
volume which goes into slabs, edgings, and sawdust. 

(h) Data on sawing practice include gage of saws, actual widths and lengths of 
lumber sawed, efficiency of sawyers, methods of sawing, and the output or per- 
formance of mill. 

(r) Data, on the character of the timber and logs measured, to indicate the 
comparison with other tracts, whether of higher or lower quality. 

6. Tables or compilation of results. The logs can be classified, first, into sound 



LUMBER GRADES AND LOG GRADES 463 

and defective. Where log grades are used, these grades are also separated. 
Next, the logs in each separate class are sorted into diameter classes, 1-inch or 2- 
inch (volume based on differences of 100 board feet was used in the studies conducted 
in District 1, Missoula, Montana). As a result of this tabulation, the logs when orig- 
inally classed by the scaler into grades by judgment, can be re-graded in accordance 
with actual specifications for the grades. A sample form of tabulation would be, 
by columns: 

Diameter class. 
Number of logs as a basis. 
Average lengths of logs. 

Per cent and value per 1000 board feet of each grade, represented in the prod- 
uct obtained. 
Total lumber tally, excluding cull lumber-sawed. 
Over-run, excluding cull lumber sawed. 
Tally of cull lumber sawed. 
Over-run, including cull lumber sawed. 
Net scale. 

Per cent of total net scale in each class of logs. 
Value per 1000 board feet, based on net tally. 
Value per 1000 board feet, based on net scale. 
Gross scale. 
Per cent deducted for defect. 

These data, shown thus for each class of logs, can be totaled for all logs, and 
averaged. 

7. Deductions or summaries. Irregularities are sure to occur in the final sum- 
maries. These can frequently be evened off by means of curves. The final curves 
and tables should show, for each separate log grade, the per cent of each grade of 
lumber obtained for logs of each diameter class, and the value of the average log for 
the class. 

Effect of Waste or Cull. Such studies indicate the effect of increasing amounts 
of waste or cull upon the value of the gross scale or log. Cull lumber may not 
reduce the sale value of the residual lumber cut from the log, but the cost of log- 
ging is based upon the actual size of the log, which is best measured by its gross 
scale. The value of the product divided by this total scale gives a more correct 
gage of the value of the whole log in terms of price per 1000 board feet, for the 
purpose of determining whether the log is merchantable. 

A crew of five men can usually tally two hundred logs per day of average 
sizes. A single mill-scale study requires from one thousand to two thousand logs 
for best results. 

Instructions for Recording Data, U. S. Forest Service. Logs should be lettered 
A, B, C, etc., A being the butt log. The species may be written out or the atlas 
number may be used, thus: " Loblolly pine " or " P76." The log length should 
be measured to the nearest tenth of a foot. The crook may be measured by noting 
the distance in inches between a straight line connecting the ends of the log on the 
concave side and the log itself. If relative terms such as " V " (very crooked), 
" M " (moderately crooked), and " S " (slightly crooked) are used, they should be 
carefully defined. Thus, if the crook is more than one-half the diameter of the log 
the term " V '' might be applied; if one-quarter to one-half the diameter it would 
be '' M'"; while less than one-quarter it would be " S." If practically straight 
indicate this by " O " after heading "' Crook." , 



464 APPENDIX A 

Form of Record for Mill-scale Studies, U. S. Forest Service 



Form 234 
Revised July 1, 1912 




Large 

END. 


Small 

END. 


Tree Log 

(Number.) (Letter.) 


D. i. b„ 1 






Width of bark, 










Log length Crook . 


.Knots 


D. o. b.. 
















1 


2 


3 


Width of sap, 
















Rings, 








Cubic ) Peeled, 






feet \ 

\ With bark, 






Full scale. 






Net scale. 






Sawad out. 




4 


5 


6 


7 


1 






2 
















3 






4 






5 






6 






7 






8 






9 






10 
11 
12 









8 


9 


10 


11 


12 













Remarks: 



Date. 



., 191 



LUMBER GRADES AND LOG GRADES 465 

Knottiness may not always be of importance, but if it is recorded letters may 
be used, as for crook. Two diameters inside bark at right angles should be measured 
and the average recorded to the nearest tenth inch. The average width of bark, 
measured on a radius, should be recorded, care being taken to make the measurements 
where bark is not partly worn off. The width of sap, in case desired, should be 
measured along an average radius. In case the age at either end of the log is found 
it can be inserted opposite " Rings." If the cubic content of a log is found in the 
office it may be entered opposite " Cubic feet." " Full scale " means the number of 
board feet that would be tallied by the log scaler if the log were straight and sound. 
" Net scale " is the number of board feet tallied by the scaler after deducting for 
defects of any kind. " Sawed out " is the number of board feet of lumber actually 
sawed out. 

The large spaces are for the dimensions of boards sawed out, each space being 
for a separate grade. The name of the grade may be written or stamped in at the 
head of the column. The total number of board feet of each grade sawed out should 
be entered opposite the proper grade number in the small spaces under " Sawed out," 
which is the grand total of these gi'ade totals. The boards may be tallied thus: 
" 1X3X16," meaning a board 1 inch thick, 3 inches wide, and 16 feet long. Frac- 
tions may be indicated thus: 3iX3-Xl2 (3|"X3|"Xl2'). As a rule the thickness 
should be recorded to the nearest even quarter inch below, the width to the nearest 
inch below, and the length to the nea^'est foot below the actual measurement. In 
some cases it may be preferable to tally the number of board feet direct. This 
means that the number of board feet in a board is read from a rule and entered at 
once. Thus for a board 1"X3"X12', the figure 3 would be tallied. 



APPENDIX B 
THE MEASUREMENT. OF PIECE PRODUCTS 

363. Basis of Measurement. Any finished products of uniform or standard dimen- 
sions, manufactured or cut from trees or logs may be measured by tallying or count- 
ing the pieces. The size or contents of the standard piece determines its value, 
either directly or by conversion to cubic or board-foot contents. The relative 
value of pieces of different sizes is seldom directly proportional to their cubic volume, 
though for such products as mining timbers this may be true. But for piling and 
poles, value per cubic foot increases with increased length. The contents of sawed 
or hewn pieces of rectangular shape is easily computed in board feet. Finished pieces 
may be classed as round, hewn, or manufactured products. Squares and bolts 
intended for further manufacture may be sold by count (§ 9). 

364. Round Products. Roum,' products include poles, piling, posts, mine 
timber, and certain lesser products such as hop poles and converter poles. Prac- 
tically all round pieces are intended for uses requiring durability against atmospheric 
and soil moisture, and strength to support weight or strains. Peeling reduces 
weight for transportation. 

Durability differs markedly with different species; hence whenever two or more 
species are available, at least two classes of product are recognized, the first con- 
taining the more durable or resistant species, the second, those which decay more 
rapidly or require preservative treatment. 

Round products are classed by length and diameter. Both minimum and maxi- 
mum specifications are quoted for length. For diameter, the minimum is given 
for each grade, since an excess adds to strength of piece. Prices are fixed by grades. 

Straightness is a quality necessary to strength, in poles and especially in piling. 
The degree of crook or sweep permitted in such products is always specified. 

A minimum taper is desired in poles and piles, especially when long, in order to 
diminish weight in handling. The diameter or circumference at both ends of poles 
and piling is specified, and both minimum and maximum limits given, corresponding 
to specified top diameters. Such limitations must coirespond to the average shape 
of the material available, both to insure strength and prevent rejection of too large' 
a percentage of pieces. 

Defects which wUl weaken the piece or decrease its durability serve to reject 
products of this character. The specifications are remarkably similar whether for 
poles, piles, mining timbers or cross ties. Such defects are shake, checks, splits, 
large coarse or rotten knots which weaken the piece, and rot. When the qualities 
of the piece for the use for which it is intended permit of knots, or of a certain amount 
of center or pipe rot, these defects may be permitted, especially if their exclusion 
would cause the rejection of a large percentage of the output. For poles, the presence 
of center rot requires an increased diameter at the butt, for acceptance of piece. 

Round products as a class give almost complete utilization of the bolt or log, and 
of the tree. The ends of piling, cross ties, and butts of poles are cut square with a 
saw, and the only waste is the bark. Where there is a market for posts or small 

466 



THE MEASUREMENT OF PIECE PRODUCTS 



467 



mine props, the tops are also utiUzed down to 3 or 4 inches. These small round prod- 
ucts also permit the utilization of suppressed trees and small timber, thus reducing 
total per cent of waste in a stand to a minimum. 

365. Poles. Standard poles are 20 feet or more in length, and are used prin- 
cipally for telegraph or telephone lines. Specifications are based usually on 
circumference rat' er than diameter. Since the ratio between the two measure- 
ments for a circle is 3.1416 to 1, and this is exceeded for eccentric cress sections, 
specifications, especially for large sizes, call for I to 1 inch greater circumference than 
the proportion of 3 to 1 for dry poles and an extra 5 to f inch for green or water- 
soaked poles. 

Whit'i cedar, which furnishes the larger part of the poles utilized, is measured 
either by circumference or diameter. The specified relation of these measurements 
for peeled poles is, 

TABLE LXVIII 
Relation between Circumference and Diameter for White Cedar Poles 



Seasoned poles, 

Top diameter. 

Inches 


Seasoned poles. 

Circumference at top. 

Inches 


Green or water-soaked poles, 

Circumference at top. 

Inches 


4 
5 
6 

7 


12 
15 

22 


16 

19i 

22| 



An excess of 6 inches in length is permitted, or 1 half-inch scant for every 5 feet 
in length. 1 

The standard specifications for Eastern white cedar poles, (American Telephone 
and Telegraph Company), are given below: 

All poles shall be reasonably straight, well proportioned from butt to top, shall 
have both ends squared, the bark peeled, and all knots and limbs closely trimmed. 

The dimensions of the poles shall be in accordance with the following table, the 
" top " measurement being the circumference at the top of the pole and the " butt " 
rasasurement the circumference, six (6) feet from the butt. The dimensions given 
are the minimum allowable circumferences at the points specified for measurement 
and are not intended to preclude the acceptance of poles of larger dimensions. 

When the dimension at the butt is not given, the poles shall be reasonably well 
proportioned throughout their entire length. No pole shall be over six (6) inches 
longer or three (3) inches shorter than the length for which it is accepted. If any 
pole is more than six (6) inches longer than is required, it shall be cut back. 

Quality and Defects of Timber. The wood of a dead pole is grayish in color. The 
presence of a black line on the edge of the sapwood (as seen on the butt) also shows 
that a pole is dead. No dead poles, and no poles having dead streaks covering more 
than one-quarter of their surface, shall be accepted under these specifications. Poles 
having dead streaks covering less than one-quarter of their surface shall have a cir- 
cumference greater than otherwise required. The increase in the circumference 
shall be sufficient to afford a cross-sectional area of sound wood equivalent to that of 
sound pieces of the same class. 

^ Northwestern Cedarmen's Association. 



468 



APPENDIX B 



TABLE LXIX 

Minimum Dimensions of White Cedae Poles in Inches 





A 


B 


C 


i 
D E 


F 


G 


Length 


1 

6 feet 6 feet 




6 feet 




6 feet 








of 


Top j from 1 Top from 


Top 


from 


Top 


from 


Top 


Top 


Top 


poles 


j butt 


butt 




butt 




butt 








(Feet) 


1 1 



















20 
22 
25 
30 
35 
40 
45 
50 
55 
60 



Circumference, Inches 



231 


33 


2U 


30 


18f 


28^ 


18i 


26 


17 


151 


23^ 


34 


2U 


31 


18f 


29^ 


18i 


27 


17 


15i 


23^ 


36 


2U 


33 


18i 


31| 


18i 


28^ 


17 


15^ 


23 § 


40 


21i 


36 


ISf 


34^ 


18i 


3U 


17 


151 


23^ 


43 


2U 


40 


ISf 


37i 


18i 


3^ 


17 


15^ 


23i 


47 


2U 


43 


ISf 


40 


181 


37i 


17 


151 


23^ 


50 


2U 


46 


18-J 


43 


18i 


40 






23i 


53 


2U 


49 


18f 


46 


18i 


43 






23 i 


56 


21i 


52 














23i 


59 


2U 


54 















12* 



No dark red or copper-colored poles, which when scraped do not show good 
live timber, shall be accepted under these specifications. 

No poles having more than one complete twist for every twenty (20) feet in length, 
no cracked poles and no poles containing large season checks shall be accepted under 
these specifications. 

No poles having " cat faces," unless they are small and perfectly sound and the 
poles have an increased diameter at the " cat face," and no poles having " cat faces " 
near the six (6) foot mark or within ten (10) feet of their tops, shall be accepted under 
these specifications. 

No shaved poles shall be accepted under these specifications. 

No poles containing sap rot, evidence of internal rot as disclosed by a careful 
examination of all black knots, hollow knots, woodpeckers' holes, or plugged holes; 
and no poles showing evidences of having been eaten by ants, worms or grubs shall 
be accepted under these specifications except that poles containing worm or grub 
marks below the six (6) foot mark will be accepted. 

No poles having a short crook or bend, a crook or bend in two planes or a reversed 
curve shall be accepted under these specifications. The amount of sweep, measured 
between the (6) foot mark and the top of the pole, that may be present in poles accept- 
able under these specifications, is shown in the following tables : 

35-foot poles shall not have a sweep of over lOf inches. 
40-foot poles shall not have a sweep of over 12 inches. 
45-foot poles shall not have a sweep of over 9 inches. 
50-foot poles shall not have a sweep of over 10 inches. 
55-foot poles shall not have a sweep of over 11 inches. 
60-foot poles shall not have a sweep of over 12 inches. 



THE MEASUREMENT OF PIECE PRODUCTS 



469 



Poles having tops of the required dimensions must have sound tops. Poles 
having tops one (1) inch or more above the requirements in circumference may have 
one (1) pipe rot not more than one-half (^) inch in diameter. Poles with double 
tops or double hearts shall be free from rot where the two parts or hearts join. 

No poles containing ring rot (rot in the form of a complete or partial ring) shall 
be accepted under these specifications. Poles having hollow hearts may be accepted 
under the conditions shown in the following table : 



Average diameter 


Add 


TO Butt Requirements 








or rot 


of 25 and 30-foot 


of 35-, 40- and 45- 


of 50-, 55-, 60- and 




poles 


foot poles 


65-foot poles 


2 mches 


Nothing 


Nothing 


Nothing 


3 inches 


1 inch 


Nothing 


Nothing 


4 inches 


2 inches 


Nothing 


Nothing 


5 inches 


3 inches 


1 inch 


Nothing 


6 inches 


4 inches 


2 inches 


1 inch 


7 inches 


Reject 


4 inches 


2 inches 


8 inches 


Reject 


6 inches 


3 inches 


9 inches 


Reject 


Reject 


4 inches 


10 inches 


Reject 


Reject 


5 inches 


11 inches 


Reject 


Reject 


7 inches 


12 inches 


Reject 


Reject 


9 inches 


13 inches 


Reject 


Reject 


Reject 



Scattered rot, unless it is near the outside of the pole, may be estimated as being 
the same as heart rot of equal area. 

Poles with cup shakes (checks in the form of rings) which also have heart or star 
checks may be considered as equal to poles having hollow hearts of the average 
diameter of the cup shakes. 

Western Red Cedar forms the main source of supply of poles in the West. The 
specifications for these poles permit a much smaller taper than for Eastern timber 
since the tree form is more cylindrical. 

The specifications (American Telephone and Telegraph Company) are given 
in Table LXX, p. 470. 

For Southern Yellow Pine poles for creosoting, the required dimensions are 
given in Table LXXI, p. 471. 

Chestnut has been a standard pole timber but is rapidly disappearing in Eastern 
states because of the ravages of the chestnut blight. The specifications differ only 
slightly from those for white cedar, and are as follows: 

Dimensions. Length. Poles shall not be over six (6) inc;hes shorter or twenty- 
four (24) inches longer than the length specified in the order. 

Circumference. Poles shall be classified with respect to their circumferences at 
six (6) feet above the butt and at their top in accordance with Table LXXII, p. 
472. This table gives the minimum allowable circumference at six (6) feet above 
the butt and at the top for poles of each class and length listed and shall not preclude 
the acceptance of poles having greater circumferences at those points of measure- 
ment than those given in the table. 



470 



APPENDIX B 



TABLE LXX 

(MiNiMnM Dimensions op Western Red Cedar Poles in Inches) 

CLASSES 





A 


B 


C 


D 


E 


F 




(Minimum 


(Minimum 


(Minimum 


(Minirrium 






Length 

of 

poles 

(Feet) 


top circum- 
ference 
28). 
Circumfer- 


top circum- 
ference 
25). 
Circumfer- 


top circum- 
ference 
22). 
Circumfer- 


top circum- 
ference 
18i). 
Circumfer- 


(Minimum 
top circum- 
ference 

15) 


(Minimum 
top circum- 
ference 

12) 


ence 6 feet 


ence 6 feet 


ence 6 feet 


ence 6 feet 




from butt 


from butt 


from butt 


from butt 








Inches 


20 


30 


28 


26 


24 


No butt 


No butt 


22 


32 


30 


27 


25 


require- 


require- 


25 


34 


31 


28 


26 


ment 


ment 


30 


37 


34 


30 


28 






35 


40 


36 


32 


30 






40 


43 


38 


34 


32 






45 


45 


40 


36 


34 






50 


47 


42 


38 


36 






55 


49 


44 


40 


38 






60 


52 


46 


41 


39 






65 


54 


48 


43 









(Chestnut poles, continued) Shape. No poles shall contain short crooks. 

With respect to other deviations from straightness, poles required in the order to be 
of the " town " class, shall be free from all deviations from straightness except sweep 
in one plane only. The amount of sweep between the top and the butt of these poles 
shall not be greater than that specified for their length in the Table LXXIII, p. 472. 

Poles required by the order to be of " country " class may have sweep in two 
planes or sweep in two directions in one plane provided that a straight line con- 
necting the center of the butt with the center of the top does not, at any intermediate 
point, pass through the external surfaces of the pole. Where sweep is in one plane 
and one direction only, the amount between the top and the butt shall not be greater 
than that specified for the length of the pole in Table LXXIV, p. 473. 

366. Piling. All piles are peeled before measuring. Piling should show close 
grain or slow growth, and be straight, with a minimum taper. If a straight line 
drawn between the centers of the butt and top falls outside the peeled pile at any 
point the piece is usually rejected. Hence long piling brings a proportionally higher 
price. Specifications for piling prescribe minimum and maximum diameters for 
the butt, and a minimum top diameter. Examples of such specifications are shown 
in Table LXXV, p. 473. 

Piling is sold by the linear foot, but the price per foot increases with length of 
stick. In Southern pine, piling is frequently measured by log scale, by taking the 
diameter at the middle of the log. 



THE MEASUREMENT OF PIECE PRODUCTS 



471 



TABLE LXXI 

Minimum Dimensions of Southern Yellow Pine Poles in Inches- 
Classes 





A 


B 


C 


D 


E 


Length 






















of 




6 feet 




6 feet 




6 feet 




6 feet 




6 feet 


poles 


Top 


from 


Top 


from 


Top 


from 


Top 


from 


Top 


from 


(Feet) 




butt 




butt 




butt 




butt 




butt 




Circumference, Inches 


20 


22 


291 


20 


27 


18 


26 


16 


24 


14 


21 


22 


22 


30i 


20 


28 


18 


27 


16 


25 


14 


22 


25 


22 


32 i 


20 


29 § 


18 


28^ 


16 


26 


14 


23 


30 


22 


35 


20 


32 


18 


30i 


16 


28^ 


14 


241 


35 


22 


38 


20 


34 


18 


32i 


16 


30 


14 


26 


40 


22 


40 


20 


36 


18 


34| 


16 


32 


14 


27i 


45 


24 


421 


22 


38 


20 


36 


18 


33 f 






50 


24 


44i 


22 


40 


20 


38 


18 


35 






55 


24 


47 


22 


42i 


20 


40 










60 


24 


49 


22 


44 i 


20 


42 










65 


24 


51 


22 


47 














70 


24 


53 


22 


49 














75 


24 


55 


22 


51 














80 


24 


57 


















85 


24 


59 


















90 


24 


61 



















Defects. Defects in piling are rot, loose or rotten knots, wind shake, twisted 
grain, checks or other defects which interfere with driving or durability. 

367. Posts, Large Posts and Small Poles. Standard fence posts are cut, 7, 7^ 
or 8 feet long. Dimensions up to 10 feet are termed large posts, while lengths of 
12 to 18 feet inclusive are small poles; the distinction being based partly on the 
uses to which they are put. Standard cedar posts may be 2 inches short, and j 
inch scant in diameter when seasoned, but rtiust be full if green or water-soaked. 

Posts are graded by inch classes measured at top or small end. They will permit 
knots and other defects which will not weaken the piece for the purpose of a post. 
Cedar may contain a certain amount of center or pipe rot. White cedar posts may 
have a sweep of 4 inches. Western juniper and red cedar posts may have much 
greater sweep, provided it lies in one plane or " crooks one way." 

Post material in round bolts whose diameter exceeds 6 to 7 inches, when not 
needed for corner or gate posts, is usually split into two or more fence posts whose 
cross-sectional area will equal or exceed that of round posts of the standard dimen- 
sions. 

Posts must be cut from live timber and, in white cedar, rot or other defects are 
permitted which do not impair the strength of the post for uses of a fence post. 



472 



APPENDIX B 



TABLE LXXII 

Minimum Circumferenc-cs of Chestnut Poles in Inches 

Classes 





A 


B 


C 


D 


E 


F 


G 


Length 




























(Feet) 




6 feet 




6 feet 




6 feet 




6 feet 




6 feet 




6 feet 






Top 


from 
butt 


Top 


from 
butt 


Top 


from 
butt 


Top 


from 
butt 


Top 


from 
butt 


Top 


from Top 
butt 

1 












Inches 






20 


24 


34 


22 


31 


20 


29 


18 


27 


16 


24 


15 


1 
22 ! 15 


25 


24 


37 


22 


34 


20 


32 


18 


29 


16 


27 


15 


24 '■ 15 


30 


24 


40 


22 


37 


20 


35 


18 


32 


16 


29 


15 


27 1 15 


35 


24 


43 


22 


40 


20 


37 


18 


35 


16 


32 


15 


29 


15 


40 


24 


46 


22 


43 


20 


40 


18 


37 


16 


35 


15 


32 


15 


45 


24 


49 


22 


46 


20 


43 


18 


40 


16 


37 








50 


24 


52 


22 


49 


20 


46 


18 


43 












55 


24 


55 


22 


52 


20 


49 
















60 


24 


58 


22 


55 




















65 


26 


60 


22 


58 




















70 


26 


62 


22 


60 




















75 


26 


64 


22 


62 




















80 


26 


66 


22 


64 




















85 


26 


68 


22 


66 




















90 


26 


70 


22 


68 





















TABLE LXXIII 

Maximum Sweep, Poles, Standard 



Length 


Maximum 


Length 


Maximum 


Length 


Maximum 


of pole. 


sweep. 


of pole. 


sweep. 


of pole. 


sweep. 


Feet 


Inches 


Feet 


Inches 


Feet 


Inches 


20 


4 


45 


9 


70 


14 


25 


5 


50 


10 


75 


15 


30 


6 


55 


11 


80 


16 


35 


7 


60 


12 


85 


17 


40 


8 


65 


13 


90 


18 



Small cedar poles up to and including 18 feet in length may have a sweep of 
4 inches, which for lengths of 16 to 18 feet is measured from a point 4 feet from the 
butt, in the manner jjrescribed for long poles. 

Fire-killed lodgepole pine is accepted for jjoles and posts in the Rocky Mountains. 



THE MEASUREMENT OF PIECE PRODUCTS 



473 



TABLE LXXIV 
Maximum Sweep, Poles, Country 



Length 


Maximum 


Length 


Maximum 


Length 


Maximum 


of pole. 


sweep . 


of pole. 


sweep . 


of pole. 


sweep. 


Feet 


Inches 


Feet 


Inches 


Feet 


Inches 


20 


6 


45 


13i 


70 


21 


25 


n 


50 


15 


75 


22i 


30 


9 


55 


16i 


80 


24 


35 


10^ 


60 


18 


85 


25i 


40 


12 


65 


19i 


90 


27 



TABLE LXXV 
Dimensions for Piling 



Species, region or 
purchaser 


Length. 
Feet 


Minimum top 

diameter — Inches 

Not less than 


Diameter limits, 
butt- 
Inches 


Hardwoods — Eastern 


20-35 

40-50 
Under 30 

30-50 
Under 60 
Over 60 
Under 30 

30-^0 

40-69 
70 and over 


6 
6 
6 
6 
9 
9 
9 
9 
8 
8 


12 and over 

14 and over 

12 to 16 


California 


12 to 18 

13 to 17 


Southern Pacific R.R 

A., T. &S. F. R.R 


13 to 20 

13 to 18 

14 to 18 
14 to 18 
16 to 18 



All classes of poles and posts are usually seasoned to decrease weight for trans- 
portation. 

Fence stays are round or split pieces about 2 inches in diameter and 5 to 6 feet 
long. They are used between posts for wire fences as upright pieces not set in the 
ground, to which the wires are stapled to prevent their being spread apart by stock, 
and to reduce the number of posts required. 

Converter poles, called also furnace poles and brands, are consumed in the process 
of refinmg copper. The Montana specifications call for poles with a top diameter of 
3 to 4 inches and length of 24 feet. They should have as little taper as possible. 
Eastern brass mills use poles 25 to 40 feet long, 2 inches and over at top, and 5 inches 
and over at butt. The bark is not removed and poles must be green. 

Standard California hop poles are made from split pieces 2 by 2 inches by 8 feet. 
In the East hop poles are usually made from round pieces of approximately the same 
dimensions. 

368. Mine Timbers. Mine timber can be classed as stuUs and props, lagging, 
shaft timbers and lumber, and mine ties. StuUs include round props used as posts, 
caps to connect pairs of opposite posts, and girts to connect posts lengthwise of the 



474 APPENDIX B 

gallery. Their dimensions depend on size of galleries. Diameters vary from 5| 
to 24 inches. Square props are used for similar purposes. Small round props used 
principally in coal mines are termed mine props and run from 4 inches up in diam- 
eter and from 4 to 10 feet in length. These timbers are used to support the ground 
and must be straight, sound and free from knots that will impair the strength of 
the piece, or from defects affecting strength or durability. 

Mine timber is bought by the linear foot, by classes based on top diameter. 
Split props must have a cross-sectional area in square inches equal to that of a round 
post of minimum specified diameter. 

Pole lagging varies from I5 to 5 inches in diameter at small end and averages 16 
feet in length. Four- to five-inch poles may be split. Lodgepole pine is the 
principal species used. Lagging is bought by the piece. 

Mine Ties. Cross ties for mine tramways are usually 5 to 5^ feet long but may 
be from 3 feet to 6 feet in length, and vary for individual mines, from 3 by 4 inches 
to 5 by 6 inches in diameter. Their small size makes a market for very small timber, 
which can be grown in 20 to 30 years. Ties are bought by count, and on basis of 
specifications. 

Round mine timber of these classes and mine ties not only utilize the entire stick, 
but permit the almost complete utilization of the felled tree and of the stand. In 
fact, the tendency is to exploit young second-growth stands while still too small to 
bear seed, and under private management forests in mining regions are rapidly 
destroyed. The same conditions permit of thinnings in dense stands, the removal 
of small diseased trees and a short rotation, and under forest management offer 
very favorable conditions for profitable production of timber. 

369. Cross Ties. Standard railroad cross ties are either hewn, with two parallel 
faces, or sawed to specified dimensions. Switch ties are sawed in sets of graduated 
lengths. Hewn ties, termed also pole ties, are made from round bolts hewn on two 
sides to produce parallel faces. Bolts 14 inches and over in diameter are usually 
split into two or more ties, hewn on four sides. Hewn ties are preferred to sawed 
ties as they are said to be more durable. 

The standard specifications for cross ties of the U. S. Railroad Administration 
have since March, 1920, been adopted with slight changes by over two-thirds of the 
railroad mileage of the country. These specifications are shown graphically in Fig. 
88. The specifications of the Pennsylvania Railroad System, based on the above, 
are as follows: 

All ties shall be free from any defects that may imi)air their strength or durability 
as cross ties, such as decay,' splits, shakes, large or numerous holes - or knots, ^ or 
oblique fiber with slope greater than one in fifteen. 

Ties from needle-leaved trees shall be of compact wood with not less than one- 

1 Ties must be rejected when decayed in the slightest degree, except that the 
following may be allowed: in cedar, " pipe or stump rot " up to I5 inches diameter 
and 15 inches deep; in cypress, " peck " up to the limitations as to holes; and, in 
pine, " blue sap stain." 

2 A large hole in woods other than cedar is one more than \ inch in diameter and 
3 inches deep within, or one more than 1 inch in diameter and 3 inches deep outside 
the sections of the tie between 20 and 40 inches from its middle. Numerous holes 
are any number equaling a large hole in damaging effect. 

' A large knot is one exceeding in width more than \ of the width of the surface 
on which it appears; but such a knot may be allowed if it occurs outside the sections 
of the tie between 20 and 40 inches from its middle. Numerous knots are any 
number equaling a large knot in damaging effect. 



, i 



THE MEASUREMENT OF PIECE PRODUCTS 



475 



third summerwood when averaging five or more rings of annual growth per inch, or 
with not less than one-half summerwood in fewer rings, measured along any radius 
from the pith to the top of the tie. Ties of coarse wood, with fewer rings or less 
summerwood, will be accepted when specially ordered. 



^i 





-S- 




^^Xo>i 


1 


1 D 1 


^J 




^Tl 


L,^ 










^i 




^.i\ 


L^ 



1 



kiy lo I 



11 

a t 

o .1 . 



< 



k-i 




Ties for use without preservative treatment shall not have sapwood wider than 
one-fourth the width of the top of the tie between 20 and 40 inches from the middle, 
and will be designated as " heart " ties. Those with more sapwood will be desig- 
nated as " sap " ties. 

Manufacture. Ties should be made from trees which have been felled not longer 
than one month. 



476 



APPENDIX B 



All ties shall be straight, well manufactured, ^ cut square at the ends, have bottom 
and top parallel, and have bark entirely removed. 

Dimensions. Before manufacturing ties, producers should ascertain which of 
the following grades will be accepted. 

All ties shall be eight (8) feet six (6) inches long. 

All ties shall measure as follows throughout both sections between 20 and 40 
inches from the middle of the tie. 



Grade 


Sawed or hewn top, 
bottom and sides 


Sawed or hewn top 
and bottom 


1 
2 

3 

4 
5 


None accepted 

6" thick X7" wide on top 

6" thick X_8" wide on top 

7" thick X8" wide on top 
7" thick X9" wide on top 


6" thick X6" wide on top 
6" thick X7" wide on top 
7" thick X6" wide on top 
7" thick X7" wide on top 
6" thick X8" wide on top 
7" thick X8" wide on top 
7" thick X9" wide on top 



The above are minimum dimensions. Ties over one (1) inch more in thickness, 
over three (3) inches more in width, or over two (2) inches more in length will be 
degraded or rejected. 

The top of the tie is the plane farthest from the pith of the tree, whether or not 
the pith is present in the tie. 

Class U — Ties which May Be Used Untreated 



Group Va 


Group Vb 


Group Vc 


Group Vd 


"Heart" Black Locust 
"Heart" White Oaks 
"Heart" Black Walnut 


"Heart" Douglas Fir 
" Heart" Pines 


" Heart" Cedars 
" Heart" Cypress 
"Heart" Redwood 


" Heart" Catalpa 
"Heart" Chestnut 
"Heart" Red Mulberry 
"Heart" Sassafras 



Class T — Ties which Should Be Treated 



Group Ta 


Group T6 


Group Tc 


Group Td 


Ashes 


"Sap" Cedars 


Beech 


"Sap" Catalpa 


Hickories 


"Sap" Cypress 


Birches 


"Sap" Chestnut 


"Sap" Black Locust 


"Sap" Douglas Fir 


Cherries 


Elms 


Honey Locust 


Hemlock 


Gums 


Hackberry 


Red Oaks 


Larches 


Hard Maples 


Soft Maples 


"Sap" White Oaks 


"Sap" Pines 




"Sap" Mulberries 


"Sap" Black Walnut 


"Sap" Redwood 




"Sap" Sassafras 
Spruces 
Sycamore 
White Walnut 



1 A tie is not well manufactured when its surfaces are cut into with score-marks 
more than § inch deep or when its surfaces are not even. . 



THE MEASUREMENT OF PIECE PRODUCTS 477 

370. Inspection and Measurement of Piece Products. Piece products, while 
graded on basis of dimensions, may be rejected either because of scant length, thick- 
ness or width, below requirements for lowest grade, or because of disqualifying 
defects. As these products are usually hauled to track or landing before being 
graded, considerable losses are occasioned by failure to conform to these specifi- 
cations. 

Although the character and amount of defect disqualifying a piece is usually pre- 
scribed as exactly as possible in the specifications, yet there is always considerable 
latitude exercised by the inspector, and the closeness or laxity of inspection may 
vary under instructions according to the demand for the product. This method of 
regulating supply supplements price adjustments and is open to serious objec- 
tions. Good inspectors are thoroughly familiar with the qualities required of 
product and display a certain leniency in judging pieces which almost conform to 
specifications, provided the general run of the product is of good quality and work- 
manship. An inspector must command respect for his integrity and reputation for 
giving both parties a square deal. 

The contents of various classes of piece products may be desired in terms of either 
cubic feet or board feet, in order to reduce different kinds of products to terms of a 
common standard or to simplify terms of payment or of record. Since most of these 
products are exposed to decay, and their value is measured by their resistance to 
fungus attacks, wood preservation is becoming more prevalent. Creosoting plants 
base their charges upon the cubic contents of such pieces as are treated as a whole. 

The volume in cubic feet of poles of different dimensions is obtained by the for- 
mula; given in § 27 by applying the values for cubic volumes of cylinders shown in 
Table LXXVII, Appendix C. The middle diameter measurement is the most 
accurate method for long poles, owing to the errors resulting from large butts. 

For short poles, piling or mining stulls, the middle diameter measurement is 
probably the most satisfactory, and the table of cylindrical contents, or Humphrey 
caliper cordwood rule will suffice as a standard. Prices for mining stulls of different 
lengths and diameters sold by the U. S. Forest Service in Montana, are based 
upon the cubic contents of pieces of each standard size. 

Smaller material such as fence posts or other round pieces may be converted to 
cubic feet by the same means. 

Cross ties, on account of uniformity of size, are converted into their equivalent 
in board feet, and expressed either by average contents per tie, or by the number of 
ties per 1000 feet B. M. The average contents of hewn ties may be obtained by 
scaling a large number as logs 8 feet long. Or their cubic contents may be cal- 
culated from the thickness and face and reduced to board feet. The first method 
deducts for sawdust, and the second for squaring the tie. By either method a 6- by 
8- inch tie scales about 32 board feet, or 30 ties per 1000 feet B.M. Ties 8^ feet long, 
7 inches thick by 9- inch face may average 40 to 44 board feet, or 25 to 23 per 1000 
board feet. 

Ratios are easily worked out on the basis of specifications and actual scale, and, 
once determined, may be substituted for measurement and applied to the count of 
ties, separately for each size class or grade of tie. 

To reduce piling to board feet, pieces are sometimes scaled directly by a log rule. 
For small poles, posts or mining timbers the best method of conversion is to apply 
a converting factor to the cubic contents of pieces of given dimensions. Where 
total or actual cubic contents is measured, the best ratio is probably 5.5 board feet 
per cubic foot. If cubic contents includes only the cylinder measured at small end, 
a larger ratio is required. 



478 



APPENDIX B 



The following table gives converting factors adopted by the U. S. Forest Service 
for products of various classes and dimensions : 



TABLE LXXVI 
Converting Factors, Piece Products to Board Feet 



Product 



Long cord (acid wood, 
pulpwood, and dis- 
tillation wood) 

Cord (spruce pulp- 
wood) 

Cord (shingle bolts) . . . 

Cord (fuel material 
averaging 5 inches or 
less in middle diame- 
ter) 

Cord (fuel material 
averaging 6 inches or 
more in middle diam- 
eter) 

Load (in the rough)*. . 

Pole (telephone) 

Pole (telephone) 

Pile ' 

StuU 

Tie (standard) 

Tie (2d class) 

Tie (narrow gauge) . . . 

Tie (narrow gauge) . . . 

Tie (narrow gauge) . . . 

Tie 

Tie 

Derrick pole 

Derrick set (II pieces) 



Assumed 
dimensions 



4' X5' X8' 

4' X4' X8' 

4' X4' X8' 

4' X4' X8' 



4' X4' X8' 



4' X4' X8' 
1 cord 
7"X30' 
9"X30' 
7"X30' 
10"X16' 
6"X8"X8' 
6"X7"X8' 
6"X7"X6' 
7"X8"X6r 
6"X7"X6J' 
7"X8"X8' 
7"X9"X8' 
7"X30' 



Equiv- 
alent in 
board 
feet 



625 

560 
600 
333 J 



333J 
60 

100 
60 
60 
30 
20 
15 
25 
15 
30 
35 
60 

480 



Product 



Trestle timber 

Trestle timber 

House log 

House log 

House log 

Mining timber 

Prop 

Converter pole 

Pole (fence) 

Pole (fence) 

Lagging (6 pieces) . . . 
Cubic foot (round) . . . 

Rail (split) 

Piece 

Stick 

Slab 

Post 

Post (circumference, 

18 inches) 

Post 

Linear foot 

Brace 

Stay (fence) 

Stay 

Shake (roof) 

Shake (fruit tray) .... 

Picket 

Stake (fence) 



Assumed 
dimensions 



10"X20' 
7"X12' 
8"X16' 
X16' 
XIO' 
XIO' 
XIO' 
X20' 



7'' 
7" 
6'' 
6'' 
4" 
16' 
4"X20' 
3"X6' 



i pole 

6"X7' 

6"X7' 

2"X6"X16' 

6"X7' 



5.7"xr 
5" XT 
10" XI' 
4"X6' 
2"X6' 
4"X6' 



'X6"X2' 
'X5"X32" 
'X5' 
'X5' 



Equiv- 
alent in 
board 
feet 



70 

20 

30 

30 

15 

10 

10 

10 

8 

10 

10 

6 

5 

7 

7 

2 

7 

6 
5 
3 
2 



* This refers to small irregular pieces of wood and not to material that can be ricked for 
measurement. 



APPENDIX C 
TABLES USED IN FOREST MENSURATION 

TABLE LXXVII 

Cubic Contents of Cylinders and Multiple Table of 

Basal Area 

This table serves a double purpose. It shows, in the first place, 
the contents of cylinders of different diameters and lengths. It may be 
used to determine the contents of logs whose diameters are measured 
at the middle. The table shows also the sums of the basal areas of 
different numbers of trees. Thus the total basal area of fifty-one 
trees 9 inches in diameter is 22.53 square feet. This table will be found 
very useful in computing the total basal area of different diameter 
classes in forest surveys. 

The values given in this table are practically identical with those 
of the Humphrey Caliper Cordwood Rule (§ 121) for which it may be 
substituted. By multiplying the values in the table by 1.28 the 
contents of logs will be found in terms of stacked cubic feet of cord- 
wood, p. 480. 

TABLE LXXX 

The International Log Rule for Saws Cutting a j inch 

Kerf 

This log rule is derived from the values of the International log 
rule for saws cutting a |-inch kerf, by applying the factor .904762 to 
the values in the former rule, computing to the third decimal place, 
and then rounding off the resultant values to the nearest 5 board feet. 
The values were computed and checked by Judson F. Clark in 1917, 
p. 493. 

TABLE LXXXIi 

Values in square feet for .16 and for .66 of the area of circles of dif- 
ferent diameters, for computing the cubic volume of trees by the Schiffel 
formula, F=(.16 B-\-Mb) h, p. 494. 

1 Computed by the U. S. Forest Service. 

479 



480 



APPENDIX C 



TABLE LXXVII 

Cubic Contents of Cylinders and Multiple Table op Basal Areas 









Diameter in In 


:hes. 






Length, 
















Feet, or 


'4 


3 


4 


5 


! 6 


7 


8 


Number 










1 






of Trees. 
















Contents of Cylinders in Cubic Feet, or 


Basal Areas in Square 


Feet. 


I 


0.02 


0.05 


0.09 


0.14 


0. 20 


0.27 


0.35 


2 


0.04 


0. 10 


0.17 


0.27 


0.39 


0.53 


0. 70 


3 


0.07 


0.15 


0.26 


0,41 


0.59 


0.80 


I 05 


4 


0.09 


0.20 


0.35 


0.55 


0.79 


1.07 


I .40 


5 


0. II 


0.25 


0.44 


0.68 


98 


1-34 


1-75 


6 


0. I,^ 


0. 29 


0.52 


0.82 


I. 18 


1 .60 


2.09 


7 


0.15 


0-34 


0.61 


0.95 


1-37 


. 1.87 


2.44 


8 


0. 17 


0-39 


0. 70 


•I .09 


1-57 


2.14 


2,79 


9 


0. 20 


0.44 


0.79 


1.23 


1-77 


2.41 


314 


ID 


0. 22 


0.49 


0.87 


1.36 


I .96 


2.67 


3-49 


II 


0.24 


0.54 


0.96 


1.50 


2.16 


2.94 


3.84 


12 


0. 26 


0.59 


1.05 


1.64 


2.36 


3-21 


4.19 


13 


0.28 


0.64 


I-I3 


1.77 


2-55 


3-47 


4-54 


14 


0.31 


0.69 


1 .22 


I. 91 


2-75 


3-74 


4.89 


15 


0.33 


074 


1.31 


2.05 


2-95 


4.01 


5 24 


i6 


. 35 


0.79 


1 .40 


2.18 


3-14 


4.28 


5-59 


17 


0.37 


0.83 


1.48 


2 32 


3 • 34 


4-54 


5.93 


18 


0.39 


0.88 


1-57 


2.45 


3-53 


4.81 


6.28 


19 


0.41 


0.93 


1.66 


2.59 


3-73 


5.08 


6.63 


20 


0.44 


0.98 


1-75 


2-73 


3-93 


5-35 


6.98 


21 


0.46 


I 03 


1.83 


2.86 


4.12 


5-6i 


7-33 


22 


0.4S 


1 .08 


1.92 


3.00 


4 32 


5.88 


7.68 


23 


0.50 


113 


2 .01 


314 


4-52 


6.15 


8.03 


24 


0.52 


1. 18 


2.09 


3-27 


471 


6.4 


8.38 


25 


0.55 


1-23 


2.18 


3-41 


4.91 


6.68 


8.73 


26 


0.57 


1.28 


2.27 


3-55 


5 II 


6.95 


9.08 


27 


0.59 


I • 33 


2.36 


3.68 


5 • 30 


7.22 


9.42 


28 


0.61 


1-37 


2.44 


3.82 


5 50 


7.48 


9-77 


29 


. 63 


1.42 


2.53 


3-95 


5.69 


7-75 


10. 12 


30 


0.65 


1-47 


2.62 


4.09 


5-89 


8.02 


10.47 


31 


■ 0.68 


1.52 


2.71 


4-23 


6.09 


8. 28 


10.82 


32 


0. 70 


1-57 


2.79 


4 36 


6.28 


8.55 


II. 17 


33 


0.72 


1.62 


2.88 


4 50 


6.48 


8.82 


11-52 


34 


0.74 


1.67 


2.97 


4.64 


6.68 


0.09 


II .87 


35 


0. 76 


I .72 


3 05 


4 77 


6.87 


9-35 


12 . 22 


36 


0.79 


I -77 


3- 14 


491 


7.07 


9.62 


• 2 57 


37 


0.81 


I .82 


3-23 


5.05 


7 . 26 


9. 89 


12.92 



TABLES USED IN FOREST MENSURATION 



481 



TABLE LXXYU—Continued 









Diameter in Inches. 






Length, 
















Feet, or 


3 


3 


4 


5 


6 


7 


8 


Number 
of Trees. 
















Contents of Cylir 


ders in Cubic Feet, or 


Basal Areas in Square 


Fe.t. 


38 


0.83 


1.87 


3-32 


5.18 


7.46 


10. 16 


13.26 


39 


0.85 


I. 91 


3 40 


5-32 


7.66 


10.42 


13.61 


40 


0.87 


1 .96 


3-49 


5-45 


7.85 


10.69 


1 3 - 96 


41 


0.89 


2.01 


3.58 


5 • 59 


8.05 


10.96 


14-31 


42 


0.92 


2.06 


3.67 


5-73 


8.25 


11.22 


14.66 


43 


0.94 


2.11 


3-75 


5.86 


8.44 


II .49 


15.01 


44 


0.96 


2.16 


3-84 


6.00 


8.64 


11.76 


15-36 


45 


0.98 


2.21 


3 • 93 


6.14 


8.84 


12.03 


15-71 


46 


I .00 


2.26 


4.01 


6.27 


903 


12.29 


16.06 


47 


1.03 


231 


4. 10 


6.41 


9-23 


12.56 


16.41 


48 


1.05 


2.36 


4.19 


6.54 


9.42 


12.83 


16.76 


49 


1.07 


2-4I 


4.28 


6 . 68 


9.62 


13.10 


17 . 10 


50 


1.09 


2-45 


4.36 


6.82 


9.82 


13.36 


17.45 


51 


I . 1 1 


2.50 


4-45 


6.95 


10.01 


13.63 


17.80 


52 


113 


2.55 


4-5 + 


7.09 


10.21 


13.90 


18.15 


53 


I. 16 


2.60 


4.63 


7-23 


10.41 


14.16 


/8.50 


54 


I. 18 


2.65 


. 4-71 


7.36 


10.60 


14.43 


18.85 


55 


I . 20 


2.70 


4.80 


7 -50 


10.80 


14.70 


19. 20 


56 


I .22 ■ 


2-75 


4.89 


7.64 


1 1 .00 


14.97 


19.55 


57 


1.24 


2.80 


4-97 


7-77 


1 1 . 19 


15.23 


19.90 


58 


1.27 


2.85 


5.06 


7-91 


1 1 • 39 


15.50 


20.25 


59 


1.29 


2.90 


515 


8.04 


11.58 


15-77 


20.60 


60 


1 31 


2-95 


5 24 


8. 18 


II .78 


16.04 


20.94 


61 


1-33 


2.99 


5 • 32 


8.32 


11.98 


16. :(0 


21 .29 


62 


1-35 


304 


541 


8.45 


12.17 


16.57 


2i .64 


63 


1-37 


3 09 


5 50 


8.59 


12.37 


16.84 


21 .99 


64 


1.40 


3-14 


5-59 


8.73 


12.57 


17.10 


2 . M 


65 


1.42 


3- 19 


5 67 


8.86 


12.76 


17-37 


2 .69 


66 


1.44 


3-24 


576 


9.00 


12 .96 


17.64 


23.04 


67 


1.46 


3 29 


5.85 


914 


13.16 


17.91 


2 3 -,^9 


68 


1.48 


3 • 34 


5 93 


9.27 


13.35 


18.17 


23-74 


69 


1-51 


3 • 39 


6.02 


9.41 


13.55 


18.44 


24.09 


70 


I 53 


3-44 


6. II 


9-54 


13.74 


18.71 


24-43 


71 


I 55 


3-49 


6. 20 


9 . 68 


13-94 


18.97 


24.78 


72 


1-57 


3-54 


6.28 


9.82 


14. 14 


19.24 


25-13 


73 


1-59 


3-58 


6.37 


9-95 


14.33 


19.51 


25-48 


74 


1. 61 


3.63 


6.46 


10.09 


14.53 


19.78 


25 ■ 83 


75 


1.64 


3.68 


6.54 


10. 23 


14.73 


20.04 


26.18 



482 



APPENDIX C 



TABLE LXXYU— Continued 





Diameter in Inches. 


Length. 
















Feet, or 


9 


10 


11 


12 


13 


14 


15 


Number 
of Trees. 
































Conte 


nts of Cylinders in Cubic Feet, or 


Basal Areas 


in Square 


Feet. 


I 


0.44 


0-55 


0.66 


0.79 


0.92 


1.07 


1-23 


2 


0.88 


1 .09 


1-32 


1-57 


1.84 


2.14 


2-45 


3 


1-33 


, I .64 


1.98 


2.36 


2.77 


3-21 


3-68 


4 


1-77 


2.18 


2.64 


3-14 


3-69 


4.28 


4.91 


5 


2.21 


2.73 


3-30 


3-93 


4.61 


5-35 


6. 14 


6 


2.65 


3-27 


3-96 


4-71 


5-53 


6.41 


7.36 


7 


3 09 


3-82 


4.62 


5-50 


6-45 


7-48 


8-59 


8 


3-53 


4-36 


5.28 


6.28 


7-37 


8-55 


9.82 


9 


3 98 


4.91 


5-94 


7.07 


8.30 


9.62 


11 .04 


lO 


4.42 


5-45 


6.60 


7-85 


9.22 


10.69 


12.27 


II 


4.86 


6.00 


7.26 


8.64 


10. 14 


11 . 76 


13-50 


12 


5.30 


6.55 


7.92 


9-42 


1 1 .06 


1 2 . 83 


14-73 


13 


5-74 


7.09 


8.58 


10.21 


11.98 


13.90 


15-95 


14 


6. 19 


7.64 


9-24 


1 1 .00 


12.90 


14-97 


17.18 


15 


6.63 


8.18 


9.90 


11.78 


13-83 


16.04 


18.41 


i6 


7.07 


8-73 


10.56 


12.57 


14-75 


17 . 10 


19.63 


17 


751 


9.27 


II .22 


13-35 


15-67 


18. 17 


20.86 


i8 


7-95 


9.82 


11.88 


14.14 


16.59 


19.24 


22 .09 


19 


8.39 


10.36 


12.54 


14.92 


1751 


20.31 


23-32 


20 


8.84 


10.91 


13.20 


15-71 


18.44 


21.38 


24-54 


21 


9.28 


11-45 


13-86 


16.49 


19-36 


22.45 


25-77 


22 


972 


12 .00 


14-52 


17.28 


20.28 


23-52 


27.00 


23 


10. 16 


12.54 


15.18 


18.06 


21 .20 


24-59 


28.23 


24 


10.60 


13-09 


15-84 


18.85 


22. 12 


25 - 66 


29-45 


25 


II .04 


13-64 


16.50 


19.64 


23.04 


26.73 


30.68 


26 


11.49 


14.18 


17 . 16 


20.42 


23-97 


27.79 


31-91 


27 


11-93 


14-73 


17-82 


21.21 


24-89 


28.86 


33-13 


28 


12.37 


15-27 


18.48 


21.99 


25.81 


29-93 


34-36 


29 


12.81 


15.82 


19. 14 


22.78 


26.73 


31.00 


35-59 


30 


1325 


16.36 


19.80 


23-56 


27.65 


32-07 


36.82 


31 


13- 70 


16.91 


20.46 


24-35 


28.57 


33-14 


38.04 


32 


14.14 


17-45 


21.12 


25-13 


29.50 


34-21 


39-27 


33 


14-58 


18.00 


21.78 


25.92 


30.42 


35 - 28 


40.50 


34 


15.02 


18.54 


22.44 


26.70 


31-34 


36 - 35 


41.72 


35 


15-46 


19.09 


23.10 


27-49 


32.26 


37-42 


42.95 


36 


15 90 


19.64 


23.76 


28.27 


33-18 


38 . 48 


44-18 


37 


16.35 


20.18 


24.42 


29.06 


34-10 


39-55 


45 41 



TABLES USED IN FOREST MENSURATION 



483 



TABLE LXXYII— Continued 





Diameter in Inches. 


Length, 
















Feet, or 


9 


10 


11 


13 


13 


14 


15 


Number 
















of Trees. 
































Contents of Cylinders in Cubic Feet, or 


Basal Areas in Square 


Feet. 


38 


16.79 


20.73 


25.08 


29-85 


35-03 


40.62 


46.63 


39 


17-23 


21 .27 


25-74 


30.63 


35-95 


41.69 


47.86 


40 


17.67 


21.82 


26.40 


31-42 


36.87 


42-76 


49.09 


41 


18. II 


22.36 


27.06 


32.20 


37 - 79 


43-83 


50.31 


42 


18.56 


22.91 


27.72 


32.99 


38.71 


44.90 


51-54 


43 


19.00 


23-45 


28.38 


33-77 


39.64 


45.97 


52-77 


44 


1944 


24.00 


29.04 


34 - 56 


40.56 


47.04 


54.00 


45 


19.88 


24-54 


29.70 


35 - 34 


41.48 


48.11 


55.22 


46 


20.32 


25.09 


30 . 36 


36.13 


42.40 


49-17 


56.45 


47 


20.76 


25-63 


31.02 


36-91 


43-32 


50.24 


57.68 


48 


21.21 


26.18 


31.68 


37 - 70 


44.24 


51-31 


58.90 


49 


21.65 


26.73 


32-34 


38.48 


45-17 


52.38 


60.13 


50 


22 .09 


27.27 


33 00 


39-27 


46.09 


53-45 


61.36 


51 


22.53 


27.82 


33.66 


40.06 


47.01 


54-52 


62.59 


52 


22.97 


28.36 


34-32 


40.84 


47-93 


55-59 


63.81 


53 


23-41 


28.91 


34.98 


41 -63 


48.85 


56 . 66 


65.04 


54 


23.86 


29-45 


35 - 64 


42.41 


49-77 


57 - 73 


66.27 


55 


24 ■ .30 


30.00 


36 . 30 


43.20 


50.70 


58.80 


67.49 


56 


24-74 


30.54 


36 - 96 


43-98 


51.62 


59-86 


68.72 


57 


25.18 


31.08 


37-62 


44-77 


52-54 


60.93 


69.95 


58 


25-62 


31-63 


38.28 


45-55 


53-46 


62.00 


71.18 


59 


26.07 


32.18 


38.94 


46 . 34 


54-38 


63.07 


72.40 


60 


26.51 


32.73 


39.60 


47.12 


55-31 


64.14 


73.63 


61 


26.95 


33-27 


40.26 


47-91 


56.23 


65.21 


74.86 


62 


27.39 


33-82 


40.92 


48.69 


57-15 


66.28 


76.09 


63 


27-83 


34 - 36 


41-58 


49-48 


58.07 


67 - 35 


77.31 


64 


28.27 


34-91 


42.24 


50-27 


58.99 


68.42 


78.54 


65 


28.72 


35-45 


42.90 


51-05 


59-91 


69-49 


79-77 


66 


29. 16 


36.00 


43 - 56 


51-84 


60.84 


70.55 


80.99 


67 


29.60 


36.54 


44-22 


52.62 


61.76 


71 .62 


82.22 


68 


30,04 


37-09 


44-88 


53-41 


62.68 


72.69 


83-45 


69 


30 . 48 


37.63 


45-54 


.S4 ■ rg 


63.60 


7376 


84.68 


70 


30.93 


38.18 


46.20 


54-98 


64.52 


74.83 


85.90 


71 


31-37 


38.72 


46 . 86 


55-76 


65-44 


75-90 


87.13 


72 


31.81 


39-27 


47-52 


56-55 


66.37 


76.97 


88 . 36 


73 


32.25 


39.82 


48.18 


57 - 33 


67.29 


78.04 


89.58 


74 


32-69 


40 . 36 


48.84 


58.12 


68.2 1 


79- II 


90.81 


75 


33-13 


40.91 


49 50 


58.91 


69 - 1 3 


80. 18 


92.04 



484 



APPENDIX C 



TABLE LXXYIl^Continued 





Diameter in Inches. 


Length, 
















Feet, or 


16 


17 


18 


19 


20 


21 


22 


Number 
of Trees. 
































Contents of CyHnders in Cubic Feet, or 


Basal Areas in Square 


Feet. 


I 


1.40 


I . 5S 


1.77 


I -97 


2.18 


2.41 


2.64 


2 


2.79 


3.15 


3 . 53 


3.94 


4., 36 


4.81 


5.28 


3 


4.19 


4-73 


5 -,30 


5-91 


6.54 


7 . 22 


7.92 


4 


5-59 


6.31 


7.07 


7.88 


8.73 


9.62 


10.56 


5 


6. 98 


7.88 


8.84 


9.84 


10.91 


12.03 


1 3 . 20 


6 


8 . 3-'^ 


9.46 


1 . 60 


1 1. 81 


1 3 • 09 


14.43 


15.84 


7 


9-77 


1 1 . 03 


1 2 . 37 


13-78 


15.27 


16.84 


18.48 


8 


II. 17 


12.61 


14.14 


1575 


17.45 


19.24 


21.12 


9 


12.57 


14.19 


1 5 . 90 


17.72 


19-63 


2 1 . 65 


23.76 


lO 


13-96 


15.76 


17.67 


19.69 


21 .82 


2405 


26.40 


II 


15-36 


1 7 . 34 


19.44 


21 .66 


24.00 


26.46 


29.04 


12 


16.76 


18.92 


21.21 


23-63 


26.18 


28.86 


31-68 


13 


18.15 


20.49 


22.97 


25.60 


28.36 


31 .27 


,34-32 


14 


19-55 


22.07 


2474 


27.57 


30.54 


33 . 67 


36 . 96 


15 


20 . 94 


23.64 


26.51 


29-53 


32.72 


36.08 


39 ■ 60 


i6 


22.34 


25-22 


28.27 


31.50 


,34.91 


38.48 


42.24 


17 


23.74 


26.80 


30 . 04 


^V47 


37 09 


40.89 


44.88 


i8 


25-13 


28.37 


SI . 81 


.^ =i ■ 44 


.39.27 


43 - 30 


47.52 


19 


26.53 


29-95 


33.58 


37-41 


41-45 


45 70 


50. 16 


20 


27.93 


31.53 


35 . 34 


39 . 38 


43 63 


48.11 


52.80 


21 


29.32 


33-10 


37.11 


41.35 


45.82 


50.51 


55-44 


22 


30.72 


34.68 


38 . 88 


4332 


48.00 


52.92 


58.08 


23 


32.11 


36.25 


io.64 


45 29 


50.18 


55 . 32 


60.72 


24 


33-51 


37 -'^^ 


42.41 


47.25 


52.36 


57.73 


63.36 


25 


34-91 


39.41 


44.18 


49.22 


54 • 54 


60 . 1 3 


66.00 • 


26 


36 . 30 


40.98 


45 ■ 95 


51 .19 


56.72 


62.54 


68.64 


27 


37 . 70 


42.56 


47.71 


53. 16 


58 . 90 


64 ■ 94 


71.27 


28 


.^9- 10 


44.14 


49.48 


55.13 


61 .09 


67.35 


73.91 


29 


40.49 


45.71 


51.25 


57.10 


63.27 


69 -75 


76.55 


30 


41.89 


47 .29 


53 01 


59.07 


65.45 


72.16 


79- 19 


31 


43.28 


48. 86 


54.78 


6 1 . 04 


67.63 


74 ■ 56 


81.83 


32 


44.68 


50 -44 


56 . 55 


6s. 01 


69.81 


76.97 


84.47 


33 


46.08 


52.02 


58.32 


64 . 98 


71.99 


79.37 


87.11 


34 


47-47 


53 . 59 


60.08 


66 . 94 


74.18 


81 .78 


89.75 


35 


48.87 


55-17 


61.85 


68.91 


76.36 


84 . 1 8 


92.39 


36 


50.27 


56.75 


63.62 


70.88 


78.54 


86 . 59 


95-03 


37 


51.66 


58 . 32 


65 - 38 


72.85 


•80.72 


89.00 


97-67 



TABLES USED IN FOREST MENSURATION 
TABLE LXXYII— Continued 



485 



" 


Diameter in Inches. 


Length, 
















Feet, or 


16 


17 


18 


19 


20 


31 


33 


Number 
















of Trees. 
















Contents of Cylinders in Cu 


Ac Feet, or 


Basal Areas in Square 


Feet. 


38 


53 -06 


59 90 


67.15 


74.82 


82.90 


91.40 


100.31 


39 


54 • 45 


61.47 


68.92 


76.79 


85.08 


93-81 


102.95 


40 


55 -85 


63.05 


70.69 


78.76 


87.27 


96.21 


105.59 


41 


57-25 


64.63 


72.45 


80.73 


89 -45 


98.62 


108.23 


42 


58 . 64 


66. 20 


74.22 


82. 70 


91-63 


101 .02 


110.87 


43 


60.04 


67.78 


75-99 


84.66 


93-81 


103-43 


113.51 


44 


61 .44 


69 . 36 


77-75 


86.61 


95-99 


105-83 


116.15 


45 


62 . 83 


70.93 


79-52 


88.60 


98.17 


108.24 


118.79 


46 


64 23 


72.51 


81 .29 


90.57 


I 00 . 36 


110.64 


121.43 


47 


65.62 


74.08 


83.06 


92-54 


102.54 


113.05 


124.07 


48 


67.02 


75.66 


84.82 


94-51 


104.72 


115.45 


126.71 


49 


68.42 


77-24 


86.59 


96.48 


I 06 . 90 


117.86 


129.35 


50 


69.81 


78.81 


88.36 


98.45 


109.08 


120.26 


131.90 


51 


71.21 


80 . 39 


90. 12 


100.42 


III .26 


122.67 


134.63 


52 


72.61 


81.97 


91.89 


102.39 


"3-45 


125.07 


137.27 


53 


74.00 


83-54 


93.66 


104-35 


"563 


127.48 


139.91 


54 


7540 


85.12 


95-43 


106.32 


117-81 


129.89 


142.55 


55 


76.79 


86 . 69 


97-19 


108.29 


119.99 


132.29 


145.19 


56 


78.19 


88.27 


98. 96 


no. 26 


122.17 


1 34 - 70 


14/. 83 


57 


79 • 59 


89.85 


100.73 


112.23 


124-35 


137- 10 


150.47 


58 


80.98 


91.42 


102.49 


114.20 


126.54 


1 39 - 5 1 


153." 


59 


82.^8 


93.00 


104. 26 


116.17 


128.72 


141 -91 


155.75 


60 


83.78 


94.58 


1 06 . 03 


118.14 


1 30 . 90 


144.32 


158.39 


61 


85.17 


96 . 1 5 


107 .80 


120. II 


133 08 


146.72 


161.03 


62 


86.57 


97.73 


109.56 


122.07 


135-26 


149.13 


163.67 


63 


87.96 


99 . ,30 


1 1 1 ■ 33 


124.04 


137-44 


151.53 


166.31 


64 


89 . 36 


100.88 


113-10 


126.01 


139-63 


153.94 


168.95 


65 


90.76 


102.46 


1 1 4. .86 


1 27. 98 


141 -81 


156.34 


171.59 


66 


92.15 


104.03 


1 16.63 


129-95 


143-99 


158.75 


174.23 


67 


93 ■ 55 


105.61 


1 1 8 . 40 


131.92 


146.17 


161.15 


176.87 


68 


94-95 


107. 19 


120. 17 


133-89 


148.35 


163.56 


179.51 


69 


96 - 34 


108.76 


121 .93 


135-86 


150.53 


165.96 


182.15 


70 


97-74 


110.34 


123.70 


137.83 


152.72 


168.37 


184.79 


71 


99 - 1 3 


I II .91 


125.47 


1 39 . 80 


1 54 ■ 90 


170.77 


187-43 


72 


100.53 


1 1 3 . 49 


127.23 


141.76 


157.08 


173.18 


1 90 . 07 


73 


101.93 


115.07 


129.00 


143.73 


159.26 


175.59 


192.71 


74 


103.32 


1 16 ,64 


1,^0.77 


145.70 


161.44 


177.99 


195-35 


75 


104.72 


I I 8.22 


132.54 


147.67 


163.62 


1 80 . 40 


197-99 



486 



APPENDIX C 



TABLE LXXYII— Continued 





Diameter in Inches. 


Length, 
















Feet, or 
Number 


33 


24 


25 


36 


37 


38 


39 


of Trees. 



















Contents of Cylinders in Cubic Feet, or 


Basal Areas in Square 


Feet. 


I 


2.89 


3-14 


3-41 


3-69 


3-98 


4.28 


4-59 


2 


5-77 


6.28 


6.82 


7-37 


7-95 


8-55 


9.17 


3 


8.66 


9.42 


10.23 


II .06 


"-93 


12.83 


13-76 


4 


11-54 


12.57 


13-64 


14-75 


15-90 


17. 10 


18.35 


5 


14-43 


15-71 


17.04 


18.44 


19.88 


21.38 


22.93 


6 


17-31 


18.85 


20.45 


22. 12 


23-86 


25.66 


27.52 


7 


20.20 


21.99 


23-86 


25.81 


27-83 


29-93 


32.11 


8 


23-08 


25-13 


27.27 


29.50 


31.81 


34-21 


36 . 70 


9 


25-97 


28.27 


30.68 


33-18 


35-78 


38.48 


41.28 


lO 


28.85 


31-42 


34-09 


36.87 


39-76 


42.76 


45.87 


II 


31-74 


34-56 


37-50 


40.56 


43-74 


47-04 


50.46 


12 


34.62 


37-70 


40.91 


44.24 


47-71 


51-3' 


55-04 


13 


37-51 


40.84 


44-31 


47-93 


51-69 


55-59 


59-63 


14 


40.39 


43-98 


47-72 


51-62 


55-67 


59.86 


64.22 


15 


43-28 


47.12 


51-13 


55.31 


59-64 


64.14 


68.80 


i6 


46. 16 


50.27 


54-54 


58-99 


63.62 


68.42 


73-39 


17 


49-05 


53.41 


57-95 


62.68 


67.59 


72.69 


77-98 


i8 


51-93 


56.55 


61.36 


66.37 


71-57 


76.97 


82.56 


19 


54-82 


59-69 


64-77 


70.05 


75-55 


81.24 


87-15 


20 


57-71 


62.83 


68.18 


73-74 


79-52 


85-52 


91-74 


21 


60.59 


65 -97 


71-59 


77-43 


83-50 


89.80 


96 - 33 


22 


63.48 


69. II 


74-99 


81. II 


87-47 


94-07 


100.91 


23 


66.36 


72.26 


78.40 


84.80 


91-45 


98.35 


105-50 


24 


69.25 


75-40 


81. 8i 


88.49 


95 - 43 


102.63 


1 10.09 


25 


72.13 


78.54 


85.22 


92.18 


99.40 


106.90 


114.67 


26 


75-02 


81 .68 


88.63 


95-86 


103.38 


III. 18 


1 19.26 


27 


77-90 


84.82 


92.04 


99-55 


107.35 


115-45 


123-85 


28 


80.79 


87-96 


95-45 


103.24 


1 1 1 - 33 


119-73 


128.43 


29 


83-67 


91 . II 


98.86 


106.92 


"5-31 


124.01 


133-02 


30 


86.56 


94.25 


102.27 


no. 61 


119.28 


128.28 


137-61 


31 


89.44 


97.39 


105.67 


114.30 


123.26 


132.56 


142.20 


32 


92.33 


100.53 


109.08 


117.98 


127.23 


136-83 


146.78 


33 


95-21 


103.67 


112.49 


121 .67 


131-21 


141 . 1 1 


151-37 


34 


98. 10 


106.81 


115-90 


125-36 


135-19 


145-39 


155.96 


35 


100.98 


109.96 


119. 31 


129.05 


139.16 


149.66 


160.54 


36 


103.87 


113. 10 


122.72 


132-73 


143-14 


153-94 


165.13 


37 


106.75 


116.24 


126.13 


136.42 


147. II 


158.21 


169.72 



TABLES USED IN FOREST MENSURATION 
TABLE LXXYII— Continued 



487 





Diameter in Inches. 


Length, 
















Feet, or 
Number 


23 


34 


35 


36 


37 


38 


29 


of Trees. 
















Contents of Cyhnders in Cubic Feet, or 


Basal Areas in Square 


Feet. 


38 


109.64 


119.38 


129-54 


1 40 . II 


151.09 


162.49 


174-30 


39 


112.52 


122.52 


132.94 


143-79 


155-07 


166.77 


178.89 


40 


115.41 


125.66 


136.35 


147.48 


159-04 


171-04 


183-48 


41 


1 1 8 . 30 


128.81 


139-76 


151-17 


163.02 


175-32 


188.06 


42 


121. 18 


131-95 


143-17 


154-85 


167.00 


179-59 


192.65 


43 


124.07 


135-09 


146.58 


158.54 


170.97 


183-87 


197-24 


44 


126.95 


138.23 


149.99 


162 23 


174-95 


188.15 


201.83 


45 


129.84 


141-37 


153-40 


165.92 


178.92 


192.42 


206.41 


46 


132.72 


144-51 


156.8- 


169.60 


182.90 


196.70 


2 I I . 00 


47 


135-61 


147-65 


1 60 . 2 2 


173-29 


186.88 


200.97 


215.59 


48 


138.49 


I 50 . 80 


163.62 


176.98 


190.85 


205.25 


220. 17 


49 


141.38 


1 53 - 94 


167.03 


180.66 


194-83 


209.53 


224.76 


50 


144.26 


157-08 


170.44 


184.35 


198.80 


213.80 


229.35 


51 


147-15 


1 60 . 2 2 


173-85 


188.04 


202.78 


218.08 


233-93 


52 


150.03 


163-36 


177.26 


191.72 


206.76 


222.35 


238.52 


53 


152.92 


166.50 


180.67 


195-41 


210.73 


226.63 


243. 11 


54 


155.80 


169.65 


184.08 


199. 10 


214.71 


230.91 


247.69 


55 


158.69 


172.79 


187.49 


202.79 


216.68 


235.18 


252.28 


56 


161.57 


175-93 


1 90 . 90 


206.47 


222.66 


239-46 


256.87 


57 


164.46 


179-07 


194-30 


210. 16 


226.64 


243-73 


261 .46 


58 


167.34 


182.21 


197.71 


213.85 


230.61 


248.01 


266.04 


59 


170.23 


185-35 


201 . I 2 


217-53 


234-59 


252.29 


270.63 


60 


173-12 


188.50 


204.53 


221 .22 


238.56 


256.56 


275.22 


61 


176.00 


191.64 


207.94 


224.91 


242.54 


260.84 


279.80 


62 


178.89 


194.78 


211-35 


228.59 


246.52 


265.12 


284.39 


63 


181.77 


197.92 


214.76 


232.28 


250.49 


269.39 


288.98 


64 


184.66 


201 .06 


218.17 


235-97 


254-47 


273-67 


293.56 


65 


187.54 


204 . 20 


221.57 


239.66 


258.45 


277.94 


298.15 


66 


190.43 


207.34 


224.98 


243 - 34 


262 .42 


282.22 


302 . 74 


67 


193.31 


210.49 


228.39 


247-03 


266 . 40 


286.50 


307 • 32 


68 


1 96 . 20 


213-63 


231.80 


250.72 


270.37 


290.77 


311-91 


69 


199.08 


216.77 


235-21 


254-40 


274.35 


295 05 


316.50 


70 


201.97 


219.91 


238.62 


258.09 


278.33 


299.32 


321.09 


71 


204 . 85 


223-05 


242.03 


261.78 


282.30 


303 • 60 


325.67 


72 


207.74 


226. 19 


245-44 


265.46 


286.28 


307 - 88 


330 . 26 


73 


210.62 


229.34 


248.85 


269.15 


290.25 


312.15 


334.85 


74 


213-51 


232-48 


252.25 


272.84 


294.23 


316.42 


339.43 


75 


216.39 


235-62 


255-66 


276.53 


298.21 


320.70 


344-02 



488 



APPENDIX C 



TABLE LXXYIl—Conlinued 





Diameter in Inches. 


Length, 
















Feet, or 


30 


31 


32 


33 


34 


35 


36 


Number 
















of Trees. 


















Contents of Cylir 


ders in CuDic Fe^t, or 


Basal Areas in Square 


Feet. 


I 


4.91 


5-24 


5-59 


5-94 


6.30 


6.68 


7.07 


2 


9.82 


10.48 


II. 17 


11.88 


12.61 


13-36 


14.14 


3 


14-73 


15-72 


16.76 


17.82 


18.92 


20.44 


21 .21 


4 


19-63 


20.97 


22.34 


23-76 


25.22 


26.73 


28.27 


5 


24-54 


26.21 


27-93 


29.70 


31-53 


33-41 


35-34 


6 


29-45 


31-45 


33-51 


35 64 


37-83 


40.09 


42.41 


7 


34-36 


36.69 


39.10 


41-58 


44.14 


46.77 


49.48 


8 


39-27 


41-93 


44-68 


4752 


50.44 


53-45 


56.55 


9 


44.18 


47-17 


50.27 


53-46 


56-75 


60.13 


63.62 


lO 


49.09 


52.41 


55-85 


59-40 


63-05 


66.81 


70.69 


II 


54.00 


57-66 


61.44 


65-34 


69.36 


73-49 


77-75 


12 


58.90 


62.90 


67.02 


71-27 


75-66 


80. 18 


84.82 


13 


63.81 


68.14 


72.61 


77-21 


81.97 


86.86 


91.89 


14 


68.72 


73-38 


78.19 


83-15 


88.27 


93-54 


98.96 


15 


73-63 


73-62 


83-78 


89.09 


94-58 


100.22 


106.03 


16 


78.54 


83.86 


89 . 36 


95 03 


100.88 


I 06 . 9c 


113.10 


17 


83-45 


89. 10 


94-95 


100.97 


107 . ]8 


113-58 


120. 17 


18 


88 . 36 


94-35 


100.53 


1 06 . 9 1 


113-49 


120.26 


'27.23 


19 


93 27 


99-59 


106. 12 


112.85 


119.80 


126.95 


1 34 - 30 


20 


98.17 


104.83 


III .70 


118.79 


126. 10 


133-63 


141-37 


21 


1 03 . 08 


1 10.07 


117.29 


124-73 


132.41 


140.31 


148.44 


22 


107.99 


115-31 


122 .87 


1 30 . 67 


138.71 


146.99 


155-51 


23 


1 1 2 . 90 


120.55 


128.46 


136.61 


145.02 


153-67 


162.58 


24 


117.81 


1 25 -79 


134-04 


142.55 


151-32 


160.35 


169.65 


25 


122.72 


1 3 1 . 04 


139-63 


.48.49 


157 63 


167.03 


176.71 


26 


127.63 


136.28 


145-21 


154.43 


163-93 


173-71 


183.78 


27 


132.54 


141-52 


1 50 . 80 


160.37 


170.24 


1 80 . 40 


190.85 


28 


137-44 


146.76 


156.38 


166.31 


176.54 


187.08 


197.92 


29 - 


142.35 


1 5 2 . 00 


161 .97 


172.25 


182.85 


193-76 


104.99 


30 


147.26 


157-24 


167 -55 


178. 19 


189-15 


200.44 


2 1 2 . 06 


31 


152.17 


162. 48 


173-14 


184.13 


195-45 


207 . 12 


219.13 


32 


157-08 


167-73 


178.72 


190.07 


201 .76 


2 r 3 . 80 


226. 19 


33 


161 .99 


172.97 


184.31 


196.01 


208 . 06 


2 20 . 48 


233-26' 


34 


1 66 . 90 


178.21 


189.89 


201 .95 


214-37 


227.17 


240-33 


35 


171 .81 


183-45 


195 48 


207.88 


220.68 


233-85 


247.40 


36 


176.71 


188.69 


201 .06 


213.82 


226.98 


240.53 


254.47 


37 


181 .62 


193-93 


206.65 


219.76 


233-28 


247-21 


261.54 



TABLES USED IN FOREST MENSURATION 



489 



TABLE LXXVII— Continued 









Diameter in In 


:hes. 






Length , 
















Feet, or 


30 


31 


32 


33 


34 


35 


36 


Number 
















of Trees. 
















Contents of Cylin 


ders in Cubic Feet, or 


Basal Areas 


in Square 


Feet. 


38 


186.53 


1 99 . I 7 


212.2^ 


225.70 


239.59 


253 - 89 


268.61 


39 


191.44 


204.42 


217.82 


231.64 


245.89 


260.57 


275-67 


40 


196.35 


209 . 66 


223.40 


237-58 


252.20 


267-25 


282.74 


41 


201 . 26 


214.90 


228.99 


243-52 


258.50 


273-93 


2S9.81 


42 


206 . I 7 


220.14 


234.57 


249.46 


264.81 


2S0.62 


296.88 


43 


2 I I . 08 


225.38 


240. 16 


255-40 


271 . I I 


287.30 


303-95 


44 


215. 9S 


2 ^0.62 


245-74 


261.34 


277-42 


293-98 


311.02 


45 


220.89 


235.86 


251-33 


267.28 


283.72 


300 . 66 


3 1 8 . 09 


46 


225. So 


241. II 


256.^^1 


273.22 


290.03 


307 ■ 34 


325-15 


47 


2 ",o . 7 1 


246.35 


262.50 


279.16 


296-33 


314.02 


332-22 


48 


-^35.62 


251-59 


268.08 


285.10 


302.64 


320.70 


339 . 29 


49 


2 p. 53 


256.83 


273.67 


291.04 


308.94 


327.39 


346 - 36 


50 


24544 


262.07 


279-25 


296.98 


315-25 


334-07 


353-43 


51 


250.35 


267.31 


284-84 


302.92 


321.55 


340-75 


360.50 


52 


255.25 


272.55 


290.42 


308 . 86 


327-86 


347-43 


367-57 


53 


260. 16 


277.80 


296.01 


3 I 4 . 80 


334-16 


354-11 


374.63 


54 


265.07 


283.04 


301.59 


320.74 


340.47 


360.79 


381.70 


55 


269.98 


288.28 


307.18 


326.68 


,m6.77 


367-47 


388.77 


56 


274.89 


293.52 


312.76 


332.62 


353-08 


374-15 


395 • 84 


57 


279.80 


298.76 


318.35 


338.56 


359.38 


^80.84 


402.91 


58 


284.71 


304 . 00 


323-93 


344-50 


365 . 69 


387-52 


409.98 


59 


289.62 


309-24 


329.52. 


350 - 43 


371-99 


394-20 


417.05 


60 


294 -5-^ 


314-49 


335.10 


356-37 


378.30 


400 . 88 


424.11 


61 


299.43 


319-73 


340 . 69 


362.34 


384.61 


407 - 54 


431.21 


62 


304 • 3 \- 


324.97 


346.27 


368.28 


390.91 


414.22 


438.28 


63 


309.25 


330.21 


351.86 


374-22 


397-22 


420.80 


445.35 


64 


314.16 


335.45 


357-44 


380.16 


403-52 


427-58 


452.42 


65 


319.07 


340 . 69 


363-03 


386.07 


409.82 


434-29 


459.46 


66 


323.98 


345-93 


368.61 


392-04 


416.13 


440.95 


466.55 


67 


328.89 


351.18 


374-20 


397-98 


422.44 


447.63 


473-62 


68 


333.79 


356.42 


379-78 


403.92 


428.74 


454.31 


480.69 


69 


338.70 


361.66 


385.37 


409 . 86 


435.05 


460.99 


487-76 


70 


343.61 


366 . 90 


390.95 


415-77 


441-35 


467.69 


494.80 


71 


348.52 


372.14 


396.54 


421-74 


447-66 


474.35 


501.90 


72 


353-43 


377.38 


402 . 12 


427.68 


453-96 


481-03 


508.97 


73 


358-34 


^82.62 


470.71 


433-62 


460.27 


487-61 


516.04 


74 


363-25 


387.87 


413.29 


439-56 


466.57 


494-39 


523.11 


75 


368.16 


393.11 


418.88 


445.47 


472.87 


501.10 


530.14 



490 



APPENDIX C 



TABLE LXXVIII 

Areas of Circles or Table of Basal Areas for Diameters to Nearest 

TTf Inch 













•M 
























J! 




01 




V 




V 




fa 




fa 


^ 


fa 


^ 


fa 




fa 




fa 


s« 


4) 


In' , 

0) trt 


a 


■4-* Oi 


t 


1- . 

4-» Qj 


g 




iS 


^ Oj 


£ 






II 






0) 


^1 




.J 1—1 




El 




Q 


.006 


5 
2.0 


.022 


S 

3-0 


< 


5 


<J 


Q 


< 


Q 


<5 


1 .0 


.049 


4.0 


.087 


5-0 


.136 


6.0 


. 196 


. I 


.007 


. I 


.024 


. 1 


•052 


. I 


.092 


. I 


.142 


. I 


.203 


.2 


.008 


. 2 


.026 


.2 


.056 


. 2 


.096 


. 2 


• 147 


.2 


.210 


• 3 


.009 


• 3 


.029 


•3 


•059 


•3 


. lOI 


-3 


• 153 


•3 


.216 


■4 


.011 


■ 4 


.031 


■4 


.063 


•4 


. 106 


■4 


159 


■4 


.223 


1-5 


.012 


2-5 


•034 


3-5 


.067 


4-5 


no 


5 5 


.165 


65 


.230 


.6 


.014 


.6 


•037 


.6 


.071 


.6 


■115 


.6 


- 171 


.6 


• 238 


.7 


.016 


• 7 


.040 


•7 


.075 


•7 


120 


• 7 


.177 


■ 7 


•245 


.8 


.018 


.8 


•043 


.8 


.079 


.8 


.126 


.8 


.183 


.8 


.252 


.9 


.020 


■9 


.046 


■9 


.083 


•9 


■ 131 


•9 


. 190 


■9 


.260 


7.0 


. 267 


So 


•349 


9.0 


•44^ 


lO.O 


■545 


II .0 


.660 


12.0 


.785 


.1 


• 275 


. I 


■358 


. I 


•452 


. I 


.556 


. I 


.672 


. I 


799 


.2 


.283 


. 2 


.367 


.2 


.462 


.2 


567 


. 2 


.684 


. 2 


.812 


•3 


.291 


■ 3 


.376 


•3 


.472 


• 3 


•579 


. 3 


.696 


•3 


• 825 


•4 


.299 


■4 


.385 


•4 


.482 


•4 


■590 


-4 


.709 


■4 


• 839 


7-5 


• 307 


«-5 


•394 


9-5 


■492 


10.5 


.601 


11-5 


.721 


12.5 


• 852 


.6 


■ 315 


.6 


• 403 


.6 


503 


.6 


.613 


.6 


• 734 


.6 


.866 


.7 


• 323 


• 7 


• 413 


• 7 


•513 


•7 


.624 


• 7 


.747 


•7 


.880 


.8 


• 332 


.8 


.422 


.8 


•524 


.8 


.636 


.8 


• 759 


.8 


.894 


•9 


• 340 


•9 


• 432 


•9 


•535 


■9 


.648 


•9 


• 772 


• 9 


.908 


13.0 


.922 


14.0 


1 .069 


I5-0 


1.227 


16.0 


1-396 


17.0 


I 576 


18.0 


1.767 


. I 


• 936 


. I 


1 .084 


. I 


1.244 


. I 


1-414 


. I 


1-595 


. 1 


1.787 


.2 


• 950 


. 2 


1 . 100 


. 2 


1 . 260 


.2 


1^431 


. 2 


1 .614 


.2 


1.807 


.3 


• 965 


•3 


I. 115 


• 3 


1.277 


• 3 


1.449 


-3 


1.632 


•3 


1.827 


•4 


• 979 


•4 


1. 131 


•4 


1.294 


• 4 


1.467 


-4 


1. 65 1 


•4 


1.847 


13-5 


• 994 


'4-5 


I. 147 


15-5 


I. 310 


16.5 


1-485 


17-5 


1 .670 


18. s 


1.867 


.6 


1 .009 


.6 


I. 163 


.6 


1.327 


.6 


I • 503 


.6 


1.689 


.6 


1.887 


• 7 


1 .024 


• 7 


I. 179 


■7 


1^344 


• 7 


I. 521 


• 7 


1.709 


• 7 


1.907 


.8 


I 039 


.8 


I •195 


.8 


1.362 


.8 


1-539 


.8 


1.728 


.8 


1.928 


.9 


I 054 


■ 9 


1 .211 


• 9 


1-379 


•9 


1-558 


•9 


1.748 


•9 


1.948 



TABLES USED IN FOREST MENSURATION 

TABLE LXXYUI— Continued 



491 





























Si 




(U 




Si 




OJ 








V 




fe 




Uh 




fe 




tLH 




fe 




^ 


























































a V 




is 4^ 












i| 










«8 












2| 


Q 


<: 


^ 


<3 


Pi 


Q 


M 


< 


Q 


< 


19.0 


1.969 


20,0 


2.182 


21. 


2.405 


22.0 


2.640 


23.0 


2.885 


24.0 


3-142 


. I 


1.990 


. I 


2.204 


. I 


2.428 


. I 


2.664 


. 1 


2.910 


. I 


3.168 


. 2 


2.01 1 


.2 


2.226 


.2 


2.451 


. 2 


2.688 


. 2 


2.936 


. 2 


3-194 


•3 


2.032 


• 3 


2.248 


■3 


2.474 


.3 


2.712 


■3 


2.961 


-3 


3-221 


• 4 


2-053 


•4 


2.270 


•4 


2.498 


•4 


2.737 


■4 


2.986 


-4 


3-247 


19 5 


2.074 


20.5 


2.292 


21.5 


2.521 


22.5 


2.761 


23.5 


3.012 


24 -.s 


3-275 


.6 


2.095 


.6 


2.315 


.6 


2.545 


.6 


2.786 


.6 


3-038 


.6 


3-301 


• 7 


2. 117 


■7 


2.337 


•7 


2.568 


■7 


2.810 


■ 7 


3 ■ 064 


- 7 


3-328 


.8 


2.138 


.8 


2.360 


.8 


2.592 


.8 


2.835 


.8 


3.089 


.8 


3-355 


.9 


2. 160 


■9 


2.382 


■9 


2.616 


•9 


2.860 


•9 


3. "5 


-9 


3-382 





-u 




-M 




-ta 




















































fe 




fe 




(^ 




fe 




fc, 


II 


2 


U » 


CO 


U . 
-<-» CD 


-3 

nj a' 


+J (D 

g-s 




*-• (D 


2 

CO 

aw 


Q 


Q 
26.0 


3.687 


Q 


Q 


< 


P 


-< 


25.0 


3 409 


27.0 


3-976 


28.0 


4.276 


29.0 


4 587 


. I 


3-436 


. I 


3-715 


. I 


4.006 


. I 


4 ■ 307 


. I 


4-619 


.2 


3-464 


^ 2 


3-744 


. 2 


4-035 


. 2 


4-337 


. 2 


4.650 


.3 


3-491 


-3 


3-773 


-3 


4-065 


•3 


4.368 


•3 


4.682 


•4 


3-519 


-4 


3.801 


•4 


4.095 


-4 


4-399 


-4 


4.714 


25-5 


3-547 


26.5 


3-830 


27-5 


4-125 


28.5 


4 430 


29-5 


4.746 


.6 


3-574 


.6 


3.859 


.6 


.4-155 


.6 


4.461 


6 


4-779 


• 7 


3.602 


■7 


3.888 


•7 


4-185 


• 7 


4 - 493 


- 7 


4.8n 


.8 


3-631 


.8 


3-917 


.8 


4-215 


.8 


4-524 


.8 


4.844 


•9 


3.659 


.9 


3-947 


•9 


4-246 


•9 
33-0 


4-555 
5 940 


-9 


4.876 


30.0 


4.909 


31.0 


5-241 


32.0 


5 - 585 


34 


6.305 


35-0 


6.681 


36.0 


7.069 


37-0 


7-467 


38.0 


7.876 


390 


8.296 


40.0 


8-727 


41 .0 


9. 168 


42.0 


9.621 


43-0 


10.085 


44 


10.559 


45-0 


11.045 


46.0 


II -541 


47-0 


12.048 


48.0 


12.566 


49.0 


13-095 


50.0 


13-635 


51-0 


14. 186 


52.0 


14.748 


53-0 


15-321 


540 


15-904 


55-0 


16.499 


56.0 


17-104 


57-0 


17.721 


58.0 


18.348 


59 


1 8. 986 


60.0 


19-635 



















492 



APPENDIX C 



TABLE LXXIX 

Tables for the Conversion of the Metric to the English System and 

Vice Versa. 



Hectares 
to Acres. 



1=2 

2= 4 

3= 7 
4:= 9 
5=12 
6=14 
7=17 
8=19 
9=22 



47109 
94213 
41327 
88436 

35545 
82654 
29763 
76872 
23981 



Kilos to Povinds. 

I = 2 . 20462 
2= 4 40924 

3= 6.61386 

4= 8.81848 

5=11 .02310 

6=13.22772 

7=15.43234 

8=17. 63696 

9=19.84158 

Centimeters to 
Inches. 

1= .39370423 

2= .78740846 

3= I . 1811 1269 

4=1.57481692 

5=1.96852115 

6=2.36222538 

7=2.75592961 

8=3.14963384 

9 = 3-54333807 

Meters to Feet. 

1= 3.280869 
2= 6.561738 
3= 9.S42607 
4= 13- 123476 
5=16.404345 
6=19.685214 
7 = 22.966083 
8=26. 246952 
9=29.527821 



Acres to 
Hectares. 

1 = . 40467 
2= .80934 
3= 1 .21401 
4=1.61868 
5=2.02335 

6 = 2.42802 

7 = 2.83269 

8 = 3-23736 
9=3.64203 

Cubic Meters 
per Eicctare 
to Cubic Feet 
per Acre. 

2 = 

3 = 

4 = 

5 = 
6= 



14.291 
28.582 
42.873 
57-164 
71-455 
85-746 
7=100.037 
8 = 114.328 
9= 128.619 

Kilometers to 
Miles. 

1= .62137676 

2=1.24275352 

3=1 .86413028 

4=2.48550704 

5 = 3.10688380 

6 = 3.72826056 

7 = 4.34963732 

8 = 4.97101408 

9 = 5 59239084 

Cubic Meters 
to Cubic Feet. 

1= 35-315617 

2= 70.631234 

3= 105.946851 

4= 141 . 262468 

5=176.578085 

6 = 211 . 893702 

7 = 247.209319 

8 = 282.524936 
9=317.840553 



TABLES USED IN FOREST MENSURATION 



493 



TABLE LXXX 

The International, Log Rule for Saws Cutting a j-inch Kerf. 

Standard scale for seasoned lumber with rJ-inch shiinkage per 1-inch board, and saws cutting 
a i-inch kerf, or for green lumber, for saws cutting a ^-inch kerf. 













Length 


OP Log in 


Feet 












Diam. 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


Diam. 


4 






5 


5 


5 


5 


5 


5 


5 


5 


5 


10 


10 


4 


5 


' 5 


' 5 


5 


5 


10 


10 


10 


10 


10 


15 


15 


15 


15 


5 


6 


10 


10 


10 


10 


15 


15 


15 


20 


20 


20 


25 


25 


25 


6 


7 


10 


15 


15 


15 


20 


20 


25 


25 


30 


30 


35 


35 


40 


7 


8 


15 


20 


20 


25 


25 


30 


35 


35 


40 


40 


45 


50 


50 


8 


9 


20 


25 


30 


30 


35 


40 


45 


45 


50 


55 


60 


65 


70 


9 


10 


30 


35 


35 


40 


45 


50 


55 


60 


65 


70 


75 


80 


85 


10 


11 


35 


40 


45 


50 


55 


65 


70 


75 


80 


85 


95 


100 


105 


11 


12 


45 


50 


55 


65 


70 


75 


85 


90 


95 


105 


110 


120 


125 


12 


13 


55 


60 


70 


75 


85 


90 


100 


105 


115 


125 


135 


140 


150 


13 


14 


65 


70 


80 


90 


100 


105 


115 


125 


135 


145 


155 


165 


175 


14 


15 


75 


85 


95 


105 


115 


125 


135 


145 


160 


170 


180 


195 


205 


15 


16 


85 


95 


110 


120 


130 


145 


155 


170 


180 


195 


205 


220 


235 


16 


17 


95 


110 


125 


135 


150 


165 


180 


190 


205 


220 


235 


250 


265 


17 


18 


110 


125 


140 


155 


170 


185 


200 


215 


230 


250 


265 


280 


300 


18 


19 


125 


140 


155 


175 


190 


205 


225 


245 


260 


280 


300 


315 


335 


19 


20 


135 


155 


175 


195 


210 


230 


250 


270 


290 


310 


330 


350 


370 


20 


21 


155 


175 


195 


215 


235 


255 


280 


300 


320 


345 


365 


390 


410 


21 


22 


170 


190 


215 


235 


260 


285 


305 


330 


355 


380 


405 


430 


455 


22 


23 


185 


210 


235 


260 


285 


310 


335 


360 


390 


415 


445 


470 


495 


23 


24 


205 


230 


255 


285 


310 


340 


370 


395 


425 


455 


485 


515 


545 


24 


25 


220 


250 


280 


310 


340 


370 


400 


430 


460 


495 


525 


560 


590 


25 


26 


240 


275 


305 


335 


370 


400 


435 


470 


500 


535 


570 


605 


640 


26 


27 


260 


295 


330 


365 


400 


435 


470 


505 


540 


580 


615 


655 


690 


27 


28 


280 


320 


355 


395 


430 


470 


510 


545 


585 


625 


665 


705 


745 


28 


29 


305 


345 


385 


425 


465 


505 


545 


590 


630 


670 


715 


755 


800 


29 


30 


325 


370 


410 


455 


495 


540 


585 


630 


675 


720 


765 


810 


860 


30 


31 


350 


395 


440 


485 


530 


580 


625 


675 


720 


, 770 


820 


S70 


915 


31 


32 


375 


420 


470 


520 


570 


620 


670 


720 


770 


825 


875 


925 


980 


32 


33 


400 


450 


500 


555 


605 


660 


715 


765 


820 


875 


930 


985 


1045 


33 


34 


425 


480 


535 


590 


645 


700 


760 


815 


875 


930 


990 


1050 


1110 


34 


35 


450 


510 


565 


625 


685 


745 


805 


865 


925 


990 


1050 


115 


1175 


35 


36 


475 


540 


600 


665 


725 


790 


855 


920 


980 


1045 


1115 


1180 


1245 


36 


37 


505 


570 


635 


700 


770 


835 


905 


970 


1040 


1110 


1175 


1245 


1315 


37 


38 


535 


605 


670 


740 


810 


885 


955 


1025 


1095 


1170 


1245 


1315 


1390 


38 


39 


565 


635 


710 


785 


855 


930 


1005 


1080 


1155 


1235 


1310 


1390 


1465 


39 


40 


595 


670 


750 


825 


900 


980 


1060 


1140 


1220 


1300 


1380 


1460 


1 40 


40 


41 


625 


705 


785 


870 


950 


1030 


1115 


1200 


1280 


1365 


1450 


1535 


1620 


41 


42 


655 


740 


825 


910 


995 


1085 


1170 


1260 


1345 


1435 


1525 


1615 


1705 


42 


43 


690 


780 


870 


955 


1045 


1140 


1230 


1320 


1410 


1505 


1600 


1695 


1785 


43 


44 


725 


815 


910 


1005 


1095 


1195 


1290 


1385 


1480 


1580 


1675 


1775 


1870 


44 


45 


755 


855 


955 


1050 


1150 


1250 


1350 


1450 


1550 


1650 


1755 


1855 


1960 


45 


46 


795 


895 


995 


1100 


1200 


1305 


1410 


1515 


1620 


1730 


1835 


1940 


2050 


46 


47 


830 


935 


1040 


1150 


1255 


1365 


1475 


1585 


1695 


1805 


1915 


2030 


2140 


47 


48 


865 


975 


1090 


1200 


1310 


1425 


1540 


1655 


1770 


1885 


2000 


2115 


2235 


48 


49 


905 


1020 


1135 


1250 


1370 


1485 


1605 


1725 


1845 


1965 


2085 


2205 


2330 


49 


50 


940 


1060 


1185 


1305 


1425 


1550 


1675 


1795 


1920 


2045 


2175 


2300 


2425 


50 


51 


980 


1105 


1235 


1360 


1485 


1615 


1745 


1870 


2000 


2130 


2265 


2395 


2525 


51 


52 


1020 


1150 


1285 


1415 


1545 


1680 


1815 


1945 


2080 


2215 


2355 


2490 


2625 


52 


53 


1060 


1195 


1335 


1470 


1605 


1745 


1885 


2025 


2165 


2305 


2445 


2590 


2730 


53 


54 


1100 


1245 


1385 


1530 


1670 


1815 


1960 


2100 


2245 


2395 


2540 


2690 


2835 


54 


55 


1145 


1290 


1440 


1585 


1735 


1885 


2035 


2185 


2330 


2485 


2640 


2790 


2945 


55 


56 


1190 


1340 


1495 


1645 


1800 


1955 


2110 


2265 


2420 


2575 


2735 


2895 


3050 


56 


57 


1230 


1390 


1550 


1705 


1865 


2025 


2185 


2345 


2510 


2670 


2835 


3000 


3165 


57 


58 


1275 


1440 


1605 


1770 


1930 


2100 


2265 


2430 


2600 


2770 


2935 


3105 


3275 


58 


59 


1320 


1490 


1660 


1830 


2000 


2170 


2345 


2515 


2690 


2865 


3040 


3215 


3390 


59 


60 


1370 


1545 


1720 


1895 


2070 


2250 


2425 


2605 


2785 


2965 


3145 


3325 


3510 


60 



Formula: \(D''X0.22) -0.71D\X 0.904762 for 4-foot sections. 
Taper allowance: i inch per 4 feet lineal. 



494 



APPENDIX C 



TABLE LXXXI 

Tables for Values in Schiffel's Formula for Cubic Volumes of Entire Stems. 

This tabic is for use in calculating the cubic contents of trees by a short method (Schiffel's 
formula) : 

F=i7(0.16B+0.666). 

The field measurements necessary for this calculation are the diameter breast-high and the 
diameter at the middle height of thetree. To find the volume look up 0.16 of the area corre- 
sponding to the D.B.H. of the tree. Add to this 0.66 of the area corresponding to the diameter 
at the middle height. The sum of the two multiplied by the height of the tree equals the total 
volume of the tree in cubic feet. Thus, if the total height of the tree is 62.5 feet, the diameter 
breast-high 10.4 inches, and the diameter at the middle 8.1 inches, from tables 0.16B and 0.66i> 
it is found that the areas corresponding ot these diameters are 0.094 and 0.236, respectively. 
Their sum, 0.330, multiplied by the height, 62.5, equals the volume, 20.6 cubic feet. 







0. 16 OF THE Area of 


A Circle at Breast H 


eight (0 


.165) 




Diameter. 
























1 
0.0 


0.1 


1 
0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


Inches 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


1 


0.001 


0.001 


0.001 


0.001 


0.002 


0.002 


0.002 


0.003 


0.003 


0.003 


2 


.003 


.004 


.004 


.005 


.005 


!005 


.006 


.006 


.007 


.007 


3 


.008 


.008 


.009 


.010 


.010 


.011 


.011 


.012 


.013 


.013 


4 


.014 


.015 


.015 


.016 


.017 


.018 


.018 


.019 


.020 


.021 


5 


.022 


.023 


.024 


.025 


.025 


.026 


.027 


.028 


.029 


.030 


6 


.031 


.032 


.034 


.035 


.036 


.037 


.038 


.039 


.040 


.042 


7 


.043 


.044 


.045 


.047 


.048 


.049 


.050 


.052 


.053 


.054 


8 


.056 


.057 


.059 


.060 


.062 


.063 


.065 


.066 


.068 


.069 


9 


.071 


.072 


.074 


.075 


.077 


.079 


.080 


.082 


.084 


.086 


10 


.087 


.089 


.091 


.093. 


.094 


.096 


.098 


.100 


.102 


.104 


11 


.106 


.108 


.109 


.111 


.113 


.115 


.117 


.119 


.122 


.124 


12 


.126 


.128 


.130 


.132 


.134 


.136 


.139 


.141 


.143 


.145 


13 


.147 


.150 


.152 


.154 


.157 


.159 


.161 


.164 


.166 


.169 


14 


.171 


.173 


.176 


.178 


.181 


.183 


.186 


.189 


.191 


.194 


15 


.196 


.199 


.202 


.204 


.207 


.210 


.212 


.215 


.218 


.221 


16 


.223 


.226 


.229 


.232 


.235 


.238 


.240 


.243 


.246 


249 


17 


.252 


.255 


.258 


.261 


.264 


.267 


.270 


.273 


.276 


.280 


18 


.283 


.286 


.289 


.292 


.295 


.299 


.302 


.305 


.308 


.312 


19 


.315 


.318 


.322 


.325 


.328 


.332 


.335 


.339 


.342 


.346 


20 


.349 


.353 


.356 


.360 


.363 


.367 


.370 


.374 


.378 


.381 


21 


.385 


.389 


.392 


.396 


.400 


.403 


.407 


.411 


.415 


.419 


22 


.422 


.426 


.430 


.434 


.438 


.442 


.446 


.450 


.454 


.458 


23 


.462 


.466 


.470 


.474 


.478 


.482 


.486 


.490 


.494 


.498 


24 


.503 


.507 


.511 


.515 


.520 


.524 


.528 


.532 


.537 


.541 


25 


.545 


.550 


.554 


.559 


.563 


.567 


.572 


.576 


.581 


.585 


26 


.590 


.594 


.599 


.604 


.608 


.613 


.617 


.622 


.627 


.631 


27 


.636 


.641 


.646 


.650 


.655 


.660 


.665 


.670 


.674 


.679 


28 


.684 


.689 


.694 


.699 


.704 


.709 


.714 


.719 


.724 


.729 


29 


.734 


.7.39 


.744 


.749 


.754 


.759 


.765 


.770 


.775 


.780 


30 


.785 


.791 


.796 


.801 


.806 


.812 


.817 


.822 


.828 


.833 


31 


.839 


.844 


.849 


.855 


.860 


.866 


.871 


.877 


.882 


.888 


32 


.894 


.899 


.905 


.910 


.916 


.922 


.927 


.933 


.939 


.945 


33 


.950 


.956 


.962 


.968 


.974 


.979 


.985 


.991 


.997 


1.003 


34 


1.009 


1.015 


1.021 


1.027 


1.033 


1.039 


1.045 


1.051 


1.057 


1.063 


35 


1.069 


1.075 


1.081 


1.087 


1.094 


1.100 


1.106 


1.112 


1.118 

1 


1.125 



TABLES USED IN FOREST MENSURATION 
TABLE LXXXl—Continued 



495 







0.16 


OF THE 


\rea of 


A Circle at Breast H 


EIGHT (C 


.16B) 




Diameter. 
























0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.0 


0.7 


0.8 


0.9 


Inches 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


Sq. ft. 


36 


1.131 


1.137 


1.144 


1.150 


1.150 


1.163 


1.109 


1.175 


1.182 


1.188 


37 


1.195 


1.201 


1.208 


1.214 


1.221 


1.227 


1.234 


1.240 


1.247 


1.254 


38 


1.260 


1.267 


1.273 


1.280 


1.287 


1.294 


1.300 


1.307 


1.314 


1.321 


39 


1.327 


1.334 


1.341 


1.348 


1.355 


1.302 


1.308 


1.375 


1.382 


1.389 


40 


1.396 


1.403 


1.410 


1.417 


1.424 


1.431 


1.438 


1.440 


1.453 


1.460 


41 


1.467 


1.474 


1.481 


1.488 


1.496 


1.503 


1.510 


1.517 


1.525 


1.532 


42 


1.539 


1.547 


1.554 


1.561 


1.569 


1.576 


1 . 584 


1.591 


1.599 


1.606 


43 


1.614 


1.621 


1 . 629 


1.636 


1.644 


1.651 


1 . 059 


1.667 


1.674 


1.682 


44 


1.689 


1.697 


1.705 


1.713 


1.720 


'1.728 


1 . 730 


1.744 


1.751 


1.759 


45 


1.767 


1.775 


1.783 


1.791 


1.799 


1.807 


1.815 


1.823 


1.831 


1.839 


46 


1.847 


1.855 


1.803 


1.871 


1.879 


1.887 


1 . 895 


1.903 


1.911 


1.920 


47 


1.928 


1.936 


1.944 


1.952 


1.961 


1.969 


1.977 


1.986 


1.994 


2.002 


48 


2.011 


2.019 


2.027 


2.037 


2.044 


2 . 053 


2.001 


2.070 


2.078 


2.087 


49 


2.095 


2.104 


2.112 


2.121 


2.130 


2.138 


2.147 


2.156 


2.164 


2.173 


50 


2 . 182 


2.190 


'2.199 


2.208 


2.217 


2.226 


2.234 


2.243 


2.252 


2.261 


51 


2.270 


2.279 


2.288 


2.297 


2.306 


2.315 


2.324 


2.333 


2.342 


2.351 


52 


2.360 


2 . 309 


2.378 


2.387 


2.396 


2.405 


2.414 


2.424 


2.433 


2.442 


53 


2.451 


2.461 


2.470 


2.479 


2.488 


2.498 


2.507 


2.510 


2.520 


2.535 


54 


2.545 


2.554 


2.564 


2.573 


2.583 


2.592 


2.002 


2.611 


2.021 


2.030 


55 


2 . 640 


2.649 


2.659 


2.669 


2.678 


2.088 


2 . 098 


2.707 


2.717 


2.727 


56 


2.737 


2.746 


2.756 


2.700 


2.776 


2.786 


2.790 


2.800 


2.815 


2.825 


57 


2.835 


2.845 


2.855 


2.805 


2.875 


2.885 


2.895 


2.905 


2.915 


2.926 


58 


2.936 


2.946 


2.956 


2.966 


2.976 


2.986 


2.997 


3.007 


3.017 


3.027 


59 


3.038 


3.048 


3 . 0,58 


3.069 


3.079 


3.089 


3.100 


3.110 


3.121 


3.131 


60 


3.142 


3.152 


3 . 163 


3.173 


3.184 


3.194 


3.205 


3.215 


3.226 


3.237 


61 


3.247 


3.258 


3.269 


3.279 


3 . 290 


3.301 


3.311 


3.322 


3.333 


3.344 


62 


3.355 


3.305 


3.376 


3.387 


3 . 398 


3.409 


3.420 


3.431 


3.442 


3.453 


63 


3.464 


3.475 


3.486 


3.497 


3 . 508 


3.519 


3.530 


3.541 


3.552 


3.503 


64 


3.574 


3.586 


3.597 


3.008 


3 . 019 


3.630 


3.642 


3 . 653 


3.664 


3.676 


65 


3 . 687 


3.698 


3.710 


3.721 


3.733 


3.744 


3.755 


3.767 


3.778 


3.790 


66 


3.801 


3.813 


3.824 


3.836 


3.848 


3.859 


3.871 


3.882 


3.894 


3.906 


67 


3.917 


3.929 


3.941 


3.953 


3.904 


3.976 


3.988 


4.000 


4.012 


4.023 


68 


4 . 035 


4.047 


4.059 


4.071 


4.083 


4.095 


4.107 


4.119 


4.131 


4.143 


69 


4.155 


4.107 


4.179 


4.191 


4.203 


4.215 


4.227 


4 . 239 


4.252 


4.264 


70 


4.276 


4.288 


4.301 


4.313 


4.325 


4.337 


4.350 


4.362 


4.374 


4.387 


71 


4 . 399 


4.412 


4.424 


4.436 


4 . 449 


4.461 


4.474 


4.480 


4.499 


4.511 


72 


4.524 


4.530 


4.549 


4.502 


4.574 


4.587 


4.600 


4.012 


4.625 


4.638 


73 


4.050 


4.663 


4.670 


4.089 


4.702 


4.714 


4.727 


4.740 


4.753 


4.766 


74 


4.779 


4.792 


4 . 805 


4.818 


4.831 


4.844 


4.857 


4.870 


4.883 


4.896 


75 


4.909 


4.922 


4.935 


4.948 


4.901 


4.975 


4.988 


5.001 


5.014 


5.027 


76 


5.041 


5 . 054 


5.067 


5.080 


5.094 


5.107 


5.120 


5.134 


5.147 


5.161 


77 


5.174 


5.187 


5.201 


5.214 


5 . 228 


5.241 


5.255 


5.209 


5.282 


5.296 


78 


5 . 309 


5.323 


5.337 


5.350 


5 . 304 


5.378 


5.391 


5.405 


5.419 


5.433 


79 


5.440 


5.400 


5.474 


5 . 488 


5.502 


5.515 


5.529 


5.543 


5.557 


5.571 


80 


5.585 


5.599 


5.013 


5.027 


5.041 


5.655 


5.669 


5.683 


5.097 


5.711 



496 



APPENDIX C 



TABLE LXXXI— Continued 



( 

Diameter. 


3.66 OF THE Abe 


A, OF A Circle at the Middle Height of the Thee (0.66B) 


Inches 


0.0 

Sq. ft. 


0.1 

Sq. ft. 


0,2 

Sq. ft. 


0,3 

Sq. ft. 


0.4 
Sq. ft. 


0.5 
Sq. ft. 


0,6 

Sq. ft. 


0.7 

Sq. ft. 


0,8 
Sq, ft. 


0.9 
Sq. ft. 


1 


. 004 


0.004 


0.005 


0.006 


0.007 


0.008 


0.009 


0.010 


0,012 


0.013 


2 


.014 


.010 


,017 


,019 


.021 


.023 


.024 


. 026 


,028 


.030 


3 


. 032 


.035 


.037 


,039 


.042 


.044 


.047 


.049 


.052 


.055 


4 


.058 


.061 


.004 


,067 


.070 


.073 


.076 


.080 


.083 


.086 


5 


.090 


.094 


.097 


.101 


.105 


.109 


.113 


.117 


.121 


.125 


6 


.130 


.134 


.138 


.143 


.147 


.152 


.157 


.162 


,166 


.171 


7 


.176 


.182 


.187 


,192 


.197 


.202 


.208 


,213 


,219 


.225 


8 


.230 


,230 


.242 


,248 


.254 


.260 


.266 


.273 


.279 


.285 


9 


.292 


.298 


.305 


,311 


.318 


.325 


.332 


.339 


.346 


.353 


10 


. 360 


. 367 


.375 


.382 


.389 


.397 


.405 


.412 


.420 


.428 


11 


.430 


.444 


.452 


.460 


.468 


.476 


.484 


.493 


.501 


.510 


12 


.518 


. 527 


.536 


. 545 


.554 


.563 


.572 


.581 


.590 


.599 


13 


.608 


.618 


.627 


.637 


.646 


.656 


.666 


.676 


.686 


.696 


14 


.706 


.716 


.726 


.736 


.746 


.757 


.767 


.778 


.788 


.799 


15 


.810 


.821 


.832 


.843 


.854 


.865 


.870 


.887 


.899 


.910 


1(1 


.922 


.933 


.945 


.956 


.968 


.980 


.992 


1.004 


1.016 


1.028 


17 


1.040 


1.053 


1.065 


1.077 


1.090 


1.102 


1.115 


1 . 128 


1,140 


1.153 


18 


1.166 


1.179 


1.192 


1.205 


1.219 


1.232 


1,245 


1 . 259 


1,272 


1.286 


19 


1.299 


1.313 


1.327 


1.341 


1.355 


1.369 


1,383 


1,397 


1.441 


1.426 


20 


1.440 


1.454 


1.469 


1.483 


1.498 


1.513 


1,528 


1 , .542 


1.557 


1.572 


21 


1 . 587 


1 . 003 


1.618 


1 . 033 


1 . 649 


1.664 


1.680 


1.695 


1.711 


1.726 


22 


1.742 


1 . 758 


1.774 


1.790 


1.806 


1.822 


1,839 


1,855 


1.871 


1.888 


23 


1 . 904 


1.921 


1.937 


1.954 


1.971 


1.988 


2.005 


2,022 


2,039 


2.056 


24 


2.073 


2.091 


2.108 


2.126 


2.143 


2.161 


2.178 


2,190 


2,214 


2.232 


25 


2.250 


2.268 


2.286 


2.304 


2.322 


2.341 


2.359 


2,378 


2,396 


2.415 


26 


2.433 


2.452 


2.471 


2.490 


2.. 509 


2.528 


2.547 


2 . 566 


2,585 


2.605 


27 


2.624 


2.644 


2.603 


2 . 683 


2.703 


2,722 


2 . 742 


2.762 


2.782 


2,802 


28 


2.822 


2.842 


2 . 863 


2 . 883 


2.903 


2,924 


2,944 


2,965 


2 . 986 


3,006 


29 


3.027 


3.048 


3.069 


3 . 090 


3.111 


3,133 


3,154 


3.175 


3.197 


3,218 


30 


3.240 


3.261 


3.283 


3.305 


3.327 


3,349 


3.371 


3.393 


3.415 


3.437 


31 


3.459 


3.482 


3.504 


3.527 


3.549 


3.572 


3.595 


3.617 


3.640 


3.663 


32 


3.686 


3.709 


3.732 


3.750 


3.779 


3.802 


3.826 


3.849 


3,873 


3.896 


33 


3.920 


3.944 


3.968 


3.992 


4.010 


4.040 


4,064 


4.088 


4,112 


4.137 


34 


4.161 


4.186 


4.210 


4.235 


4.200 


4 . 285 


4.309 


4.334 


4.359 


4.385 


35 


4.410 


4.435 


4.460 


4.486 


4.511 


4.537 


4.562 


4.588 


4.614 


4.639 


36 


4.665 


4.691 


4.717 


4.743 


4.769 


4 . 796 


4.822 


4.848 


4 , 875 


4.901 


37 


4.928 


4.955 


4.981 


5.008 


5.035 


5.062 


5.089 


5.116 


5,143 


5.171 


38 


5.198 


5.225 


5.2,53 


5 . 280 


5.308 


5.336 


5 . 363 


5.391 


5.419 


5.447 


39 


5.475 


5..^)03 


5.532 


5 . 500 


5.588 


5.616 


5.645 


5.673 


5.702 


5.731 


40 


5.760 


5.788 


5.G17 


5,846 


5.875 


5.904 


5.934 


5.963 


5,992 


6.022 


41 


6.051 


6.081 


0.110 


0,140 


0.170 


6.200 


6,230 


6 . 260 


0,290 


6.320 


42 


6.350 


6.380 


6.411 


6.441 


6.471 


6,. 502 


0,533 


6.563 


6,594 


6.625 


43 


6.656 


6.687 


6.718 


6.74y 


6.780 


0,812 


6,843 


6.874 


6 , 906 


6.937 


44 


6.969 


7.001 


7.033 


7.064 


7.096 


7.128 


7.160 


7.193 


7.225 


7.257 


45 


7.290 

1 


7.322 


7.354 


7.387 


7.420 


7.452 


7.485 


7.518 


7.551 


7.584 


46 


[ 7.617 


7 . 650 


7.683 


7.717 


7.750 


7.784 


7.817 


7.851 


7.884 


7.918 


47 


7.952 


7,986 


8.020 


8.054 


8.088 


8.122 


8.156 


8.190 


8.225 


8.259 


48 


8.294 


8.328 


8.363 


8.404 


8.433 


8,467 


8.502 


8.537 


8.573 


8.608 


49 


8.643 


8,678 


8.714 


8.749 


8.785 


8,820 


8.856 


8 . 892 


8.927 


8.963 


50 


8.999 


9,035 


9,072 


1 9.108 


! 9.144 


9.180 


1 9,217 


9,253 


9,290 


9,326 



TABLES USED IN FOREST MENSURATION 



497 



TABLE LXXXII 

Breast-high Form Factors 

For Various Heights and Form Classes 

Total Cubic Volume of Stem 















Form Class 














Height 


























Height 


in 




























in 


feet 


0.50 


0.525 


0.55 


0.575 


0.60 


0.625 


0.65 


0.675 


0.70 


0.725 


0.75 


0.775 


0.80 


feet 


(5-foot 




























(5-foot 


classes) 


























classes) 












Bre.\st-high Form Fa 


CTOR 












20 


0.524 


0.532 


0.541 


0.548 


0.559 


0.569 


0.581 


0.592 


0.607 


0.620 


0.641 


0.661 


0.683 


20 


25 


472 


482 


494 


504 


517 


530 


545 


560 


577 


595 


614 


635 


657 


25 


30 


443 


454 


466 


478 


494 


508 


524 


541 


559 


579 


598 


621 


643 


30 


35 


424 


436 


449 


464 


478 


494 


511 


528 


547 


568 


588 


611 


635 


35 


40 


409 


422 


437 


452 


408 


483 


501 


518 


537 


559 


580 


603 


628 


40 


45 


398 


412 


427 


442 


459 


474 


493 


510 


530 


552 


574 


597 


623 


45 


50 


389 


404 


420 


435 


451 


' 468 


487 


504 


524 


546 


569 


592 


619 


50 


55 


583 


397 


414 


429 


445 


463 


482 


499 


519 


542 


565 


588 


615 


55 


60 


378 


392 


409 


424 


441 


459 


477 


495 


515 


538 


562 


584 


612 


60 


65 


373 


388 


405 


420 


437 


455 


473 


492 


512 


535 


559 


581 


609 


65 


70 


369 


385 


401 


417 


434 


452 


470 


489 


509 


532 


556 


579 


606 


70 


75 


366 


382 


398 


415 


431 


449 


467 


487 


507 


529 


553 


577 


604 


75 


80 


364 


380 


395 


412 


429 


446 


465 


485 


505 


527 


550 


575 


603 


80 


85 


361 


378 


393 


410 


427 


444 


463 


483 


503 


525 


548 


573 


601 


85 


90 


359 


370 


392 


409 


425 


442 


401 


481 


501 


523 


546 


571 


600 


90 


95 


357 


374 


390 


407 


424 


441 


460 


479 


500 


622 


545 


570 


598 


95 


100 


356 


373 


389 


405 


423 


440 


459 


478 


499 


521 


544 


569 


597 


100 


105 


354 


371 


387 


404 


421 


439 


457 


477 


498 


520 


543 


568 


596 


105 


110 


353 


370 


386 


403 


420 


437 


456 


476 


497 


519 


542 


567 


595 


110 


115 


352 


368 


385 


402 


419 


436 


455 


475 


495 


518 


541 


566 


594 


115 


120 


350 


367 


384 


401 


417 


434 


453 


474 


494 


516 


540 


565 


593 


120 



* From table, Massatabeller fiir Traduppskattning. Tor Jonson, Stockholm, Sweden, 1918, 
p. 66, by conversion of height in meters to height in feet. 



498 



APPENDIX C 



TABLE LXXXIII* 

Weights per Cord of Timber of Various Species — 7- to 8-inch Wood 

Hardwoods 



Species 



Alder, red 

Ash, Biltmore 

Ash, black 

Ash, blue 

Ash, green 

Ash, Oregon 

Ash, pumpkin 

Ash, white (forest 

growth) 

Ash, white (second 

growth) 

Aspen 

Aspen, large tooth . . . 

Basswood 

Beech 

Birch, paper 

Birch, sweet 

Birch, yellow 

Bird's eye, yellow. . . . 
Buckthorn, cascara. . 

Butternut 

Cherry, black 

Cherry, wild red 

Chestnut 

Chinquapin, Western 
Cottonwood, black.. . 

Cucumber tree 

Dogwood, flowering. 
Dogwood, Western . . 

Elder, pale 

Elm, cork 

Elm, slippery 

Elm, white 

Gum, black 

Gum, blue 

Gum, cotton 

Gum, red 



Pounds, 
green 



4150 
4050 
4700 
4150 
4300 
4150 
4150 

4150 

4600 
• 4250 
3850 
3700 
4950 
4600 
5300 
5200 
4400 
4500 
4150 
4150 
2950 
4850 
5500 
4150 
4500 
5850 
4950 
5850 
4750 
5050 
4700 
4050 
6300 
5950 
4150 



Pounds, 
seasoned: 



2600 
365 D 
3300 
3800 
3800 
3600 
3450 

3750 

4300 
2500 
2500 
2450 
4050 
3550 
4400 
4100 
2350 
3350 
2500 
3350 
2600 
2850 
3000 
2250 
3200 
5050 
4400 
3450 
4250 
3500 
3250 
3350 
4900 
3450 
3250 



Species 



Hackberry 

Haw, pear 

Hickory, big shell bark 
Hickory, butternut.. . 
Hickory, mockernut.. 
Hickory, nutmeg .... 

Hickory, pig nut 

Hickory, shagbark. . . 

Hickory, water 

Holly, American 

Hornbeam 

Laurel, California.. . . 
Laurel, mountain .... 

Locust, black 

Locust, honey 

Madrona 

Magnolia, evergreen . 

Maple, Oregon 

Maple, red 

Maple, silver 

Maple, sugar 

Oak, burr 

Oak, C a 1 i f or n i a, 

black 

Oak, canyon live . . . . 

Oak, chestnut 

Oak, cow 

Oak, laurel 

Oak, Pacific post 

Oak, post 

Oak, red 

Oak, Spanish highland 
Oak, Spanish lowland 

Oak, water 

Oak, white 

Oak, willow 

Oak, yellow 



Pounds, 
green 



4500 
5650 
5650 
5750 
5750 
5500 
5750 
5750 
6200 
5150 
5400 
4850 
5600 
5200 
5850 
5400 
5600 
4250 
4600 
4150 
5050 
5600 

5900 
6400 
5600 
5850 
5850 
6100 
5650 
5750 
5600 
6050 
5650 
5600 
6050 
5650 



Pounds, 
seasoned 



3500 
4550 
4800 
4550 
4900 
4000 
5050 
4850 
4300 
3750 
4900 
3650 
4550 
4550 
4750 
4000 
3250 
3200 
3450 
3200 
4100 
4200 

3650 
5200 
4300 
4650 
4400 

4500 
4100 
3900 
4600 
4200 
4500 
4300 
4100 



♦From General Orders No. 63, War Department, p. 4. 



TABLES USED IN FOREST MENSURATION 



499 



TABLE LXXXIII— Continued 
Haedwoods — Continued 



Species 



Poplar, yellow 


3400 


2600 


Rhododendron, great. 


5600 


3750 


Sassafras 


3950 


3000 


Service berry 


5500 


4900 


Silver-bell tree 


3950 


3000 


Sourwood 


4750 


3750 



Pounds, 1 Pounds, 
green , seasoned |j 



Species 



Pounds, I Pounds, 
green ! seasoned 



Sumach, staghorn . . . i 3700 

Sycamore | 4700 

Umbrella, Eraser. . . . 

Willow, black 

Willow, Western black 
Witch hazel 



3200 
3400 
4250 2900 

4600 2400 

4600 j 2900 
5300 I 4300 



Conifers 



Cedar, incense 

Cedar, Port Orford. . . 
Cedar, Western red . . 

Cedar, white 

Cypress, bald 

Cypress, yellow 

Douglas fir. Pacific 

Northwest 

Douglas fir, mountain 

type 

Fir, Alpine 

Fir, amabilis 

Fir, balsam 

Fir, Noble 

Fir, white 

Hemlock, black 

Hemlock, Eastern . . . 
Hemlock, Western . . . 

Larch, Western 

Pine, Cuban 



4150 


2400 


3500 


2900 


2450 


2100 


2500 


1950 


4300 


3200 


3150 


i 


3400 


3250 


3100 


2900 


2500 


2050 


4250 


2700 


4050 


2350 


2800 


2600 


5050 


2400 


4050 


3000 


4350 


3100 


4200 


2900 


4300 


3500 


4750 


4200 



Pine, jack 

Pine, Jeffrey 

Pine, loblolly 

Pine, lodgepole 

Pine, longleaf 

Pine, Norway 

Pine, pitch 

Pine, pond 

Pine, shortleaf 

Pine, sugar 

Pine, Table Mountain 
Pine, Western white. . 
Pine, Western yellow . 

Pine, white 

Spruce, Englemann . . 

Spruce, Sitka 

Spruce, white 

Tamarack 

Yew, Western 



4500 
4250 
4750 
3500 
4550 
3800 
4850 
4400 
4500 
4500 
4850 
3500 
4150 
3500 
3500 
3250 
3300 
4250 
4850 



2800 
2600 
3600 
2700 
3950 
3200 
3200 
3750 
3500 
2500 
3450 
2800 
2650 
2500 
2200 
2400 
2650 
3550 
4200 



Two pounds of air-dried wood are equivalent to 1 pound of average hard coal. 
The above table indicates the comparative fuel value of different species of wood 
compared with coal. For anthracite, the equivalent is 2.5 pounds of dry wood 
to 1 pound of coal, or 3y pounds green wood to 1 pound coal. 



500 



APPENDIX C 



TABLE 

The Tiemann Log Rule for Saws 

This log rule is applied to the diameter inside bark at middle of 

on mill tallies, for 1-inch boards, but conforms to the formula, 

TABLE 
Tiemann 



Middle 

diameter, 

Inches 



3 

4 
5 


7 
8 
9 
10 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 



Length of 



5 


6 7 


8 


9 


10 


11 12 



13 



Contents- 

















1 


1 


1 


1 


2 


2 


2 


2 


2 


3 


3 


2 


3 


3 


4 


4 


5 


5 


6 


7 


4 


5 


6 


7 


8 


8 


9 


10 


11 


6 


7 


9 


10 


11 


13 


14 


16 


17 


8 


10 


12 


14 


16 


18 


20 


22 


24 


11 


13 


16 


19 


21 


24 


27 


29 


32 


14 


17 


21 


24 


28 


31 


34 


38 


41 


17 


21 


26 


30 


34 


39 


43 


47 


52 


21 


26 


32 


37 


42 


47 


52 


58 


63 


25 


31 


38 


44 


50 


57 


63 


69 


76 


30 


37 


45' 


52 


60 


67 


74 


82 


89 


35 


43 


52 


61 


69 


78 


87 


95 


104 


40 


50 


60 


70 


80 


90 


100 


110 


120 


46 


57 


69 


80 


91 


103 


114 


126 


137 


52 


65 


78 


91 


104 


116 


129 


142 


155 


58 


73 


87 


102 


116 


131 


145 


160 


175 


65 


81 


98 


114 


130 


146 


162 


179 


195 


72 


90 


108 


126 


144 


162 


180 


199 


217 


80 


100 


120 


140 


160 


179 


199 


219 


239 


88 


110 


132 


153 


175 


197 


219 


241 


263 


96 


120 


144 


168 


192 


216 


240 


264 


288 


105 


131 


157 


183 


209 


236 


262 


288 


314 


114 


142 


171 


199 


228 


256 


284 


313 


341 


123 


154 


185 


216 


246 


277 


308 


339 


370 


133 


166 


200 


233 


266 


299 


332 


366 


399 


143 


179 


215 


251 


286 


322 


358 


394 


430 


154 


192 


231 


269 


308 


346 


384 


423 


461 


165 


206 


247 


288 


329 


371 


412 


453 


494 


176 


220 


264 


308 


352 


396 


440 


484 


528 



1 

3 

7 

12 
18 
26 
35 
45 

56 
68 
82 
97 
113 

130 
148 
168 
189 
211 

235 
259 

285 
312 
340 

370 
400 
432 
465 
500 

535 

572 



TABLES USED IN FOREST MENSURATION 



501 



LXXXIV 

Cutting a j^-inch Kerf 

log, by caliper scale with deduction of widths of bark. It is based 

L 



B.M. = (0.751)2 _2Z)) 



16" 



LXXXIV 

Log Rule 



Log — Feet 


14 


15 


16 


17 


18, 


19 


20 


21 


22 


23 


24 


Board 


Feet 




















1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


1 


4 


4 


4 


4 


4 


5 


5 


5 


6 


6 


6 


8 


8 


9 


9 


10 


10 


11 


11 


12 


13 


13 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


22 


20 


21 


23 


24 


26 


27 


28 


30 


31 


33 


34 


28 


30 


32 


34 


36 


38 


40 


42 


44 


46 


48 


37 


40 


43 


45 


48 


51 


53 


56 


59 


61 


64 


48 


52 


55 


58 


62 


65 


69 


72 


76 


79 


82 


60 


64 


69 


73 


77 


82 


86 


90 


95 


99 


103 


74 


79 


84 


89 


94 


100 


105 


110 


116 


121 


126 


88 


94 


101 


107 


113 


120 


126 


132 


139 


145 


151 


104 


112 


119 


126 


134 


141 


149 


156 


164 


171 


178 


121 


130 


139 


147 


1.56 


165 


173 


182 


191 


199 


208 


140 


150 


160 


170 


180 


190 


200 


210 


220 


230 


240 


160 


171 


183 


194 


206 


217 


228 


240 


251 


263 


274 


ISl 


194 


207 


220 


233 


246 


259 


272 


285 


298 


310 


204 


218 


233 


247 


262 


276 


291 


305 


320 


335 


349 


228 


244 


260 


276 


292 


309 


325 


341 


358 


374 


390 


253 


271 


289 


307 


325 


343 


361 


379 


397 


415 


433 


279 


299 


319 


339 


359 


379 


399 


419 


439 


459 


478 


307 


329 


351 


.373 


395 


417 


438 


460 


482 


504 


526 


336 


360 


384 


408 


432 


456 


480 


504 


528 


552 


576 


366 


393 


419 


445 


471 


497 


523 


550 


576 


602 


628 


398 


427 


455 


483 


512 


540 


569 


597 


626 


654 


682 


431 


462 


493 


524 


554 


585 


616 


647 


678 


708 


739 


466 


499 


532 


565 


598 


632 


665 


698 


732 


765 


798 


501 


537 


.573 


609 


644 


680 


716 


752 


788 


823 


859 


538 


577 


615 


653 


692 


730 


769 


807 


846 


884 


922 


576 


618 


659 


700 


741 


782 


823 


865 


906 


947 


988 


616 


660 


704 


1 748 


792 


836 


880 


924 


968 


1012 


1056 



502 



APPENDIX C 



TABLE LXXXV 
TiEMANN Log Rule 
Reduced to end measurement assuming a taper of 1 inch to 8 feet. 



Small 


Length of Log — Feet 


end 
diameter, 


6 


1 
8 10 


12 


14 


16 


Inches 














Contents of Log — Board Feet 




4 


2 


3 


4 


6 


7 


9 


5 


4 


6 


8 


10 


12 


15 


6 


7 


9 


12 


16 


19 


23 


7 


10 


14 


18 


22 


27 


32 


8 


13 


19 


24 


30 


36 


43 


9 


18 


24 


31 


39 


47 


55 


10 


22 


31 


40 


49 


59 


69 


11 


28 


38 


49 


60 


72 


84 


12 


34 


46 


59 


72 


86 


101 


13 


40 


55 


70 


86 


102 


119 


14 


47 


64 


82 


100 


119 


139 


15 


55 


75 


95 


116 


138 


160 


16 


63 


86 


109 


133 


157 


183 


17 


72 


98 


124 


151 


178 


207 


18 


81 


110 


139 


170 


201 


233 


19 


91 


123 


156 


190 


224 


260 


20 


101 


137 


174 


211 


249 


289 


21 


112 


152 


192 


233 


276 


319 


22 


124 


167 


212 


257 


303 


351 


23 


136 


184 


232 


282 


332 


384 


24 


149 


201 


253 


307 


363 


419 


25 


162 


218 


276 


334 


394 


455 


26 


176 


237 


299 


362 


427 


493 


27 


190 


256 


323 


392 


461 


532 


28 


205 


276 


348 


422 


497 


573 


29 


221 


297 


374 


453 


533 


615 


30 


237 


318 


401 


486 


572 


659 


31 


253 


341 


429 


519 


611 


704 


32 


271 


364 


458 


554 


652 


751 



TABLES USED IN FOREST MENSURATION 503 



TABLE LXXXVI 

ScRiBNER Decimal C Log Rule for Saws Cutting a j-inch Kerf 

This log rule disregards taper, and is applied at small end of log, 
inside bark. It is based on diagrams of 1-inch boards, values not made 
regular by curves, and deduction for slab too large above 28 inches. 

The Decimal form is given, with values of the original rule rounded 
off to the nearest 10 board feet and the cipher dropped. To read in 
board feet, add the cipher. Decimal C values are given, as in 
Table XII, § 68. Values above 44 inches adopted by the U. S. Forest 
Service. 



504 



APPENDIX C 



TABLE LXXXVI 
ScRiBNER Decimal C Log Rule 



Diam- 


Length — Feet 


Diam- 


eter, 


6 1 


7 1 


8 1 


9 


10 


11 


12 


13 


14 


15 


16 


eter, 


Inches 


Contents — Board Feet 


Inches 


6 


0.5 


0.5 


0.5 


0.5 


1 


1 


1 


1 


1 


1 


2 


6 


7 


0.5 


1 


1 


1 


1 


2 


2 


2 


2 


2 


3 


7 


8 


1 


1 


1 


1 


2 


2 


2 


2 


2 


2 


3 


8 


9 


1 


2 


2 


2 


3 


3 


3 


3 


3 


3 


4 


9 


10 


2 


2 


3 


3 


3 


3 


3 


4 


4 


5 


6 


10 


11 


2 


2 


3 


3 


4 


4 


4 


5 


5 


6 


7 


11 


12 


3 


3 


4 


4 


5 


5 


6 


6 


7 


7 


8 


12 


13 


4 


4 


5 


5 


6 


7 


7 


8 


8 


9 


10 


13 


14 


4 


5 


6 


6 


7 


8 


9 


9 


10 


11 


U 


14 


15 


5 


G 


7 


8 


9 


10 


11 


12 


12 


13 


u 


15 


16 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


16 


17 


7 


8 


9 


10 


12 


13 


14 


15 


16 


17 


18 


17 


18 


8 


9 


11 


12 


13 


15 


16 


17 


19 


20 


21 


18 


19 


9 


10 


12 


13 


15 


16 


18 


19 


21 


22 


24 


19 


20 


11 


12 


U 


16 


17 


19 


21 


23 


24 


26 


28 


20 


21 


12 


13 


15 


17 


19 


21 


23 


25 


27 


28 


30 


21 


22 


13 


15 


17 


19 


21 


23 


25 


27 


29 


31 


33 


22 


23 


14 


16 


19 


21 


23 


26 


28 


31 


33 


35 


38 


23 


24 


15 


18 


21 


23 


25 


28 


30 


33 


35 


38 


40 


24 


25 


17 


20 


23 


26 


29 


31 


34 


37 


40 


43 


46 


25 


26 


19 


22 


25 


28 


31 


34 


37 


41 


44 


47 


50 


26 


27 


21 


24 


27 


31 


34 


38 


41 


44 


48 


51 


55 


27 


28 


22 


25 


29 


33 


36 


40 


44 


47 


51 


54 


58 


28 


29 


23 


27 


31 


35 


38 


42 


46 


49 


53 


57 


61 


29 


30 


25 


29 


33 


37 


41 


45 


49 


53 


57 


62 


66 


30 


31 


27 


31 


36 


40 


44 


49 


53 


58 


62 


67 


71 


31 


32 


28 


32 


37 


41 


46 


51 


55 


60 


64 


69 


74 


32 


33 


29 


34 


39 


44 


49 


54 


59 


64 


69 


73 


78 


33 


34 


30 


35 


40 


45 


50 


55 


60 


65 


70 


75 


80 


34 


35 


33 


38 


44 


49 


55 


60 


66 


71 


77 


82 


88 


35 


36 


35 


40 


46 


52 


58 


63 


69 


75 


81 


86 


92 


36 


37 


39 


45 


51 


58 


64 


71 


77 


84 


90 


96 


103 


37 


38 


40 


47 


54 


60 


67 


73 


80 


87 


93 


100 


107 


38 


39 


42 


49 


,56 


63 


70 


77 


84 


91 


98 


105 


112 


39 


40 


45 


53 


60 


68 


75 


83 


90 


98 


105 


113 


120 


40 


41 


48 


56 


64 


72 


79 


87 


95 


103 


111 


119 


127 


41 


42 


50 


59 


67 


76 


84 


92 


101 


109 


117 


126 


134 


42 


43 


52 


61 


70 


79 


87 


96 


105 


113 


122 


131 


140 


43 


44 


56 


65 


74 


83 


93 


102 


111 


120 


129 


139 


148 


44 


45 


57 


66 


76 


85 


95 


104 


114 


123 


133 


143 


152 


45 


46 


59 


69 


79 


89 


99 


109 


119 


129 


139 


149 


159 


46 


47 


62 


72 


83 


93 


104 


114 


124 


134 


145 


155 


166 


47 


48 


65 


76 


86 


97 


108 


119 


130 


140 


151 


162 


173 


48 


49 


67 


79 


90 


101 


112 


124 


135 


146 


157 


168 


180 


49 


50 


70 


82 


94 


105 


117 


129 


140 


152 


164 


175 


187 


50 



TABLES USED IN FOREST MENSURATION 505 



TABLE LXXXVII 
Index to Standard Volume Tables 

Standard volume tables (§ 140) have been constructed by the 
U. S. Forest Service, by state forestry departments, by forest schools, 
and in some instances by private corporations, or individuals. 

This index is intended to include such of these tables as are of 
value for future timber estimating, and can be obtained in published 
form, or from the U. S. Forest Service. The index briefly describes 
each table under the standard headings to enable the estimator to 
decide whether or not it is suitable for his purposes. The final column 
gives the Forest Service designation of such tables as have not so far 
been published. 



506 



APPENDIX C 



Hardwoods 



TABLE 



Species 



Locality 



Tree class 



Unit of measure- 
ment 



Log rule 



Aspen . . . . 

Aspen . . . . 

Aspen . . . . 
Aspen . . . . 
Ash, black 
Ash, black 
Ash, black 
Ash, green . 
Ash, green 
Ash, green 
Ash, gieen 
Ash, green 
Ash, green 
Ash, white 
Ash, white 
Ash, white 
Ash, white 
Ash, white 
Ash, white 
Ash, white 

Ash, white 
Ash, white 

Basswood. . . 
Beech . . . . 
Beech 

Beech 

Beech 

Beech 

Beech 

Beech 

Birch, paper . 
Birch, paper. 
Birch, paper. 
Birch, paper . 
Birch, paper. 
Birch, paper . 
Birch, paper. 
Birch, yellow 

Birch, yellow 
Birch, yellow 
Birch, yellow 
Chestnut . . . . 
Chestnut . . . . 

Chestnut. . . . 
Cottonwood . 
Cottonwood . 



New Hampshire 

Maine 

Maine 

Utah 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

General 

Eastern U. S. 

Vermont 
Vermont 

Lake States 

Vermont 

Vermont 

Michigan 
Pennsylvania 
New Hampshire 
Pennsylvania 
Michigan 
New Hampshire 
New Hampshire 
Maine, N. Hamp. 
Maine, N. Hamp. 
Maine, N. Hamp. 
Maine, N. Hamp. 
Maine, N. Hamp. 
Vermont 

Vermont 

New Hampshire 

Lake States 

Connecticut 

Connecticut 

Connecticut 
Mississippi Valley 
Mississippi Valley 



25-50 yrs. 



Over 75 yrs. 
Over 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 



Second growth 
Second growth 



45-60 yrs. 
45-60 yrs. 



Second growth 
Second growth 



Second growth 
Second growth 

Second growth 
Second giowth 
Second growth 



Cubic ft. peeled 

merch. 
Cubic ft. peeled 

merch. 
Cords 
Board ft. 

Cu. ft., peeled total 
Cords 
Board feet 
Cu. ft., peeled total 
Cu. ft., peeled total 
Cords 
Cords 
Board feet 
Board feet 
Cu. ft., peeled total 
Cu. ft., peeled total 
Cords 
Cords 
Board feet 
Board feet 
Cu. ft. of branch 

wood 
Cu. ft., with limbs 
Bd. ft. and cu. ft. in 

tops 
Board feet 
Cu. ft., with limbs 
Bd. ft. and cu. ft. in 

tops 
Cubic feet 
Cubic feet 
Board feet 
Board feet 
Board feet 
Cubic ft., merch. 
Board feet 
Cu. ft., total 
Cubic ft., merch. 
Board feet 
Cubic ft., merch. 
Board feet 
Cu. ft., total with 

limbs 
Board feet 
Board feet 
Board feet 
Cu. ft., merch. O.B. 
Board feet 

Cubic feet merch. 
Cu. ft., peeled total 
Board feet 



Scribner Dec C. 



Scribner Dec. C. 



Scribner Dec. C. 
Scribner Dec. C. 



Scribner Dec. C. 
Scribner Dec. C. 



Scribner Dec. C. 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 

Mill tally 



New Hampshire 
New Hampshire 



Scribner Dec. C. 
Scribner Dec. C. 



International 
i" kerf 



Scribner Dec. C. 



TABLES USED IN FOREST MENSURATION 



507 



LXXXVII 



Hardwoods 



D.B.H. 


Height. 


Top 
diameter. 


Basis. 


Date 


Publication 


U. S. F. S. 


(Inches) 


(Feet) 


(Inches) 


Trees 






designation 


5-13 


50- 80 





289 


1905 


Bui. 36, U. S. Forest Service 




5-20 


30- 90 


4 


362 


1911 


Bui. 93, U. S. Forest Service 




5-20 


30- 90 


4 


362 


1911 


•• 




10-27 


1-4 log 


9 


675 


1913 




W5-V10 


6-30 


60-110 




116 


1915 


Bui. 299. U. S. Dept. Agr. 




6-30 


60-110 




116 


1915 


" 




8-30 


2- 6 log 


6-12 


116 


1915 


" 




4-24 


40-100 




278 


1915 


*' 




8-44 


60-130 




918 


1915 


'• 




4-24 


40-100 




278 


1915 


" 




8-44 . 


60-130 




918 


1915 


" 






40-100 


6-10 


223 


1915 


•' 




8-44 


60-130 


6-10 


918 


1915 


" 




2-22 


20- 90 




806 


1915 


" 




6-36 


50-150 




488 


1915 


" 




4-22 


20- 90 




696 


1915 


" 




6-32 


50-120 




487 


1915 


" 




8-24 


U-5 1og 


6-18 
.2 


423 
475 


1915 
1915 
1915 


" 




3-21 


40- 90 




285 


1914 


Bui. 176, Vt. Agr. Exp. Sta. 




3-20 


40- 90 




285 


1914 






8-40 


2-4i 


6-24 


319 


1915 


Bui. 285, U. S. Dept. Agr. 




3-14 


30- 70 




102 


1914 


Bui. 176, Vt. Agr. Exp. Sta. 




3-14 


30- 70 




102 


1914 






4-26 


40-100 


6-15 


289 


1915 


Bui. 285, U. S. Dept. Agr. 




8-30 


70-110 


6-21 


120 


1909 


' ' 




7-24 


^3^ log 


6-17 


376 


1915 


' ' 




10-30 


2-4 log 


6-21 


118 


1915 


' ' 






1-4 i log 


6-15 


285 


1915 


' ' 






10-50 used 


4-10 


427 


1905 


Bui. 36, U. S. Forest Service 




6-16 


10-50 used 


4-10 ■ 


427 


1905 






4-16 


50- 90 




443 


1909 


Circ. 163, U. S. Forest Service 




5-14 


12-60 used 




396 


1909 






5-14 


12-60 used 




396 


1909 


" 




5-18 


50 - 90 












5-18 


50- 90 


3.3-6.1 


396 


1909 


Circ. 163, U. S. Forest Service 




3-15 


40- 70 






1914 






3-14 


40- 70 






1914 


■• 




7-32 


^3^ log 


6-21 


651 


1915 


Bui, 285, U. S. Dept. Agr. 




8-30 


U-3^ log 


6-17 


237 


1915 


' ' 




2-25 


20- 90 


2 


218 


1912 


Bui. 96, U. S. Forest Service 




9-25 


50- 90 


7-12 


118 


1912 






7-20 


50- 90 




517 


1905 


N. H. Forestry Com. Report 




5 30 


50-150 
80-150 


7-19 


409 
267 


1910 
1910 




W94-V8 


11 30 




W94-V8 









508 



APPENDIX C 



TABLE LXXXVII 



H ARDWOODS — Contin ued 



Species 



Eucalyptus 
(Blue gum) 

Eucalyptus 
(Blue gum) 

Gum, red 

Gum, red 

Gum, red 

Hickories 

Hickories 

Maple, red . . 

Maple, red . . 

Maple, sugar. 

Maple, sugar 



Maple, sugar . 
Maple, sugar 



Maple, sugar 
Maple, sugar 
Maple, sugar .... 

Maple, sugar 

Maple, sugar 
Oixk, chestnut 
Oak, chestnut . . 

Oak, red 

Oak, red 

Oak, red 

Oak, red 

Oak, red 

Oak, red, scarlet and 

black 
Oak, red, scarlet and 

black 

Oak, white 

Oak, white 



Oak, white New York 



Locality 



California 

California 

Southern States 
Southern States 
Southern States 
Eastern States 
Eastern States 
Massachusetts 
Massachusetts 
Vermont 
Vermont 

Lake States 
Pennsylvania 

Pennsylvania 
New Hampshire 
Lake States 
Lake States 
Lake States 
S. Appalachians 
S. Appalachians 
New Hampshire 
New Hampshire 
S. Appalachians 
S. Appalachians 
S. Appalachians 
Connecticut 

Connecticut 

Connecticut 
Connecticut 



Oak, w 
Poplar, 
Poplar, 
Poplar, 
Poplar, 
Poplar, 
Poplar, 



hite 

yellow . 
yellow . 
yellow . 
yellow . 
yellow . 
yellow . 



S. Appalachians 
S. Appalachians 
S. Appalachians 
S. Apiialachians 
S. Appalachians 
Virginia 
Virginia 



Tree class 



Unit of measure- 
ment 



Plantations 

Plantations 

Under 75 yrs. 
Over 75 yrs. 
Over 75 yrs. 



Second growth 
Second growth 
Second growth 
Second growth 



Over 75 yrs 
Over 75 yrs. 
Second growth 
Second growth 
Under 75 yrs. 
Over 75 yis. 
Over 75 yrs. 
Second growth 

Second growth 

Second growth 
Second growth 

Second growth 



1-.50 yrs. 
51-100 yrs. 
Under 100 yrs. 
Over 100 yrs. 
Second growth 
Second growth 



Cubic feet 

Board feet 

Board feet 
Board feet 
Board feet 
Cubic ft., merch. 
Cubic ft., total 
Cubic ft., merch. 
Cords 

Cu. ft., with limbs 
Bd. ft., cu. ft. in 

tops 
Cu. ft., merch. O.B. 
Cu. ft., merch. O.B. 

cu. ft. in tops 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet ■ 
Board feet 
Board feet 
Cubic ft., merch. 
Board feet 
Boaid feet 
Board feet 
Board feet 
Cubic ft., merch. 

Board feet 

Cu. ft., merch. O.B. 
Board feet 

Cu. ft., merch. O.B. 

Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cubic feet, total 
Board feet 



Log rule 



Scribner Dec. C. 

Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 

Mill tallies 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 



International 
t" kerf 



International 
kerf 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Mill tallies 
Mill tallies 

Scribner Dec. C. 



TABLES USED IN FOREST MENSURATION 



509 



-Continued 



Hardwoods — Continued 



Height. 

(Feet) 



30-160 

50-160 

1-6 log 
1-7 log 
80-140 
5-65 used 
40- 90 
20- 80 
20- 80 
40 -80 
40- 80 

50-100 
70-110 

2i-4 log 
i-4 log' 
U-4 log 
2-5 log 
1-U log 
1-5 log 
40-110 
10-50 used 
10-50 used 
40-100 
1-5 log 
40-130 
20- 80 

50- 80 

20- 80 
50- 70 

20- 60 

1-5 log 
1-5 log 
1-6 log 
1-5 log 
2-6 log 
50-100 
40-100 



Top 

diameter. 

(Inches) 



6-13 
6-23 
6-23 
4-20 



Trees 



Date 



6-17 
6-16 

6-16 
6-21 
6-17 
6-13 
7-22 
6-20 
6-20 
5- 9 
5- 9 
6-13 
6-22 
6-22 
2 

7-10 

2 
6 



6- 8 
6-14 



6-17 
5.9-7.2 



2611 1906 



685 

332 
1740 
1740 
630 
365 
397 
397 
222 
222 

305 
41 

41 

360 

278 

278 

278 

2232 

2232 

683 

683 

198 

1300 

1300 

441 

175 

293 
26 

349 

1436 
489 
102 
489 
407 
491 
480 



1906 

1904 
1904 
1904 
1910 
1910 
1915 
1915 
1914 
1914 

1915 
1915 

1915 
i915 
1915 
1915 
1915 
1913 
1913 
1905 
1905 
1914 
1914 
1914 
1913 

1913 

1913 
1913 

1905 

1903 
1913 
1913 
1913 
1913 
1907 
1907 



Publication 



Bui. 80, U. S. Forest Service 

Bui. 80 

Bui. 285, U. S. Dept. Agr. 

Bui. 176, Vt. Agr. Exp. Sta. 



Bui. 285, U. S. Dept. Agr. 



Bui. 285, U. S. Dept. Agr 

N.H. Forestry Com. Report 
" and Bui. 36, U. S. For. Serv. 

Bui. 96, U. S. Forest Service 



Bui. 36, U. S. Forest Service 



U. S. F. S. 
designation 



Bui. 36, U. S. Forest Service 



G93-V2-3 

G93-V1 

G71-V5 
G71-V7 
G71-V8 



Q68-V19 
Q68-V20 



Q61-V18 
Q61-V15 
Q61-V16 



Q82-V1 
W82-V24 
W82-V25 
W82-V26 

W82-V28 



510 



APPENDIX C 



TABLE LXXXVII 



Conifers 



Species 



Cedar, incense 

Cedar, incense 

Cedar, incense 

Cedar, western red. 

Cedar, western red. . 
Cedar, western red. . 

Cypress 

Cypress 

Douglas fir 

Douglas fir 

Douglas fir 

Douglas fir 

Douglas fir 

Douglas fir 

Douglas fir 

Douglas fir 

Fir, Amabilis 

Fir, balsam 

Fir, balsam 

Fir, balsam 

Fir, balsam 

Fir, balsam 

Fir, balsam 

Fir, balsam 

Fir, balsam 

Fir, balsam 

Fir, balsam, western 

Fir, red 

Fir, red 

Fir, red 

Fir, red 

Fir, white 

Fir, white 

Fir, white 

Fir, white 

Fir, white 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock 

Hemlock, western. . 
Hemlock, western. . 

Juniper 

Jumper 

Larch, western 



Locality 



California 
California 
California 
Puget Sd., Wash 

Idaho 
Idaho 

South Carolina 

South Carolina 
Washington, Oregon 
Washington, Oregon 
Oregon 
California 
California 
New Mexico 
Montana, Idaho 
Montana, Idaho 

Washington, Oregon 
New York, Maine 
New York 

Maine 

New Hampshire 

New York, Maine 

New Hampshire 

Northeast 

Northeast 

Quebec 

Idaho, Montana 

California 
California 
California 
California 
California 
California 
California 
California 
California 
New Hampshire 

Mich., Wis. 
New Hampshire 
Wis., Mich. 
Wis., Mich. 
Wis., Mich. 
Wis., Mich. 
Wis., Mich. 
Washington 
Washington 
Utah, Arizona 
Utah, Arizona 
Montana 



Tree class 



Second growth 



Unit of measure- 
ment 



Cubic feet, total 
Board feet 
Board feet 
Board feet 

Board feet 
Board feet 

Board feet 

Board feet 
Cu. ft., peeled total 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 

Board feet 
Cubic feet, total 
Cubic feet, peeled 

merch. 
Cubic feet, peeled 

merch. 
Cubic feet, peeled 

merch. 
Cords 
Cords 
Board feet 
Board feet 
Board feet 
Board feet 

Cubic feet, total 
Cubic feet, cords 
Board feet 
Board feet 
Cubic feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cubic feet, merch. 

Cu. ft., merch. O.B. 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cubic feet, total 
Cubic feet, total 
Cords with branches 
Cubic feet, total 



Log rule 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 

Scribner Dec. C. 
Scribner Dec. C. 

Scribner Dec. C. 

Scribner Dec. C. 



Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 



Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 



Scribner Dec. C. 



Scribner Dec. C. 
Maine 
Quebec 
Scribner Dec. C. 



Scribner Dec. C. 
Scribner Dec. C. 

Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 



Mill tally 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Vermont 
Scribner Dec. C. 



TABLES USED IN FOREST MENSURATION 



511 



— Continued 



CoNIifERS 



D.B.H. 

(Inches)' 



Height. 

(Feet) 

60-150 
2-9 log 
40^200 
Short, me- 
dium, tall 
1-6 log 
1-9 log 

1 5 log 

1 6 log 
20-220 
2-10 log 
2-15 log 
40-200 
1-10 log 
1-9 log 
1-7 log 
1-9 log 

1-51 log 
20- 80 
40- 80 

50- 90 

40- 60 

20- 80 
40- 60 
40- 80 
40- 90 
39- 91 
1-9 log 

40-150 
40-150 
40-150 
1-8 log 
40-170 
40-180 
3-10 logs 
90-220 
2-8 logs 
30- 70 

30-100 
30- 70 
30-100 
1-5 log 
50-120 
1-7 log 
4-100 
2-11 log 
50-200 
10- 20 
10- 20 
80-160 



I Top 

diameter.] ! Date 
I (Inches)! Trees 



8 11 
8-11 



6-7 

6-24 
6-25 



10 

7-11 

7-11 

7 

6 



4 

6 
5.8-6 
5.9-6.4 

4 



5.7-6, 

5.7-14, 

9-15 



4.4-6.5 

4 

4.4-6.5 
6-12 
6-12 
7-26 
6-17 




1054 
1054 



1890 
186 

441 

437 
1747 

967 
1394 



1048 
855 



372 

2173 

947 

330 

100 

2171 
100 



1866 
33 

677 
750 
752 
800 
597 
639 
366 
1114 
322 
317 



317 
542 
542 

1402 

1370 
320 

1440 
335 
495 
495 

1324 



1910 
1914 

1915 

1915 
1911 
1911 
1905 
1913 
1913 
1917 

1914 

1917 
1904 
1914 

1914 

1914 

1914 
1914 
1914 
1914 
1911 
1914 

1909 
1912 
1912 
1912 
1905 
1905 

1913 
1913 
1905 

1915 
1905 
1915 
1915 
1915 
1915 
1910 
1912 
1900 
1900 
1900 
1907 



Manual for Timber Reconnaisance, 

Dist. 1, U. S. Forest Service 
Bui. 272, U. S. Dept. Agr. 



Circ. 175, U. S. Forest Service 



Circ. 175, V. S. Forest Service 



M^anual for Timber Reconnaisance, 
Dist. 1, U. S. Forest Service 



Bui. 55, U. S. Dept. Agr. 



T6-V3 



T6-V3 



D1-V18 
D4-V32 
D4-V31 
D1-V35-36 
D1-V29 

A8-V2 
A-35-V2 



For Quar., IX, 593 
Manual for Timber Reconnaissance, 
Dist. 1, U. S. Forest Service 



For. Quar., XI, 362 

For. Com. N. H., 1905; Bui. 152 

U. S. Dept. Agr. 
Bui. 152, U. S, Dept. Agr. 



Bui. 161, Vt. Agr. Exp. Sta. 
Circ. 197, U. S. Forest Service 



A1-V4 

A1-V6-7 

A1-V2 

A1-V3 

A2-V3 

A2-V2 

A2-V5 

A2-V15 

A2-V17 



H65-V20 



H6-V5 
H6-V4 



L7-V3 



512 



APPENDIX C 



TABLE LXXXVII 



Conifers — Continued 



Species 



Larch, western . 
Larch, western. 
Larch, western. 



Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine, 
Pine 
Pine 
Pine, 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 
Pine 



Jack . . . . 
Jack . . . . 
Jack . . . . 
Jack . . . . 
Jeffrey. . . 
loblolly . . 
loblolly. . 
loblolly. . 
loblolly . . 
loblolly . . 
loblolly . . 
loblolly . . 
loblolly . . 
loblolly . . 
loblolly. . 
loblolly. . 
lodgepcle 
lodgepolc 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
lodgepole 
longleaf . . 

red 

red 

red 

red 

red 

red 

scrub . . . . 
scrub . . . . 
scrub . . . . 
shortleaf . 
shortleaf . 
shortleaf.. 
shortleaf . 
sugar . . . . 
sugar . . . 
sugar . . . 
white . . . . 
white . . . . 
white . . . . 
white . . . . 
white . . . . 
white . . . . 
white . . . . 
white . . . . 
white . . . . 
white . . . . 



Locality 



Montana 
Montana 
Montana 

Minnesota 

Minnesota 

Minnesota 

Minnesota 

California 

Maryland, Virginia 

Maryland, Virginia 

Maryland, Virginia 

Maryland, Virginia 

North Carolina 

North Carolina 

North Carolina 

North Carolina 

North Carolina 

North Carolina 

North Carolina 

Montana 

Montana 

Montana 

Montana ' 

Montana 

Oregon 

Oregon 

Oregon 

Oregon 

Colorado, Wyoming 

Alabama 

Minnesota 

Minnesota 

Minnesota 

Minnesota 

Minnesota 

Minnesota 

Maryland 

Maryland 

Maryland 

North Carolina 

North Carolina 

Arkansas 

Arkansas 

California 

California 

California 

New Hampshire 

Massachusetts 

Massachusetts 

New Hampshire 

Massachusetts 

Minnesota 

Minnesota 

Minnesota 

New Hampshire 

8. Appalachians 



Tree class 



Unit i>f measure- 
ment 



Under 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 
Under 75 yrs. 
Over 75 yrs. 



Under 130 yrs. 
Over 200 yrs. 
Second growth 
Second growth 
Second growth 



Second growth 
Second growth 
Second growth 
Second growth 
Second growth 
Original 
Original 
Original 
Second growth 
Under 75 yrs. 



Board feet 
Board feet 
Board feet 

Cu. ft., pesled total 
Cu. ft., merch. O.B. 
Board feet 
Board feet 
Board feet 
Cu. ft., merch. O.B. 
Peeled 
Board feet 
Board feet 
Cu. ft., peeled merch. 
Boaid feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cubic feet, merch. 
Board feet 
Board feet 
Cubic ft., total O.B. 
Board feet 
Board feet 
Poles 
Ties 

Board feet 
Board feet 
Board feet 
Cu. ft., peeled total 
Board feet 
Board feet 
Cubic feet, total 
Board feet 
Board feet 
Cords O.B. 
Cords, peeled 
Cu. ft., total O.B. 
Cubic feet, merch. 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cubic feet, merch. 
Cu. ft., total O.B. 
Cu. ft., merch O. B, 
Cords 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cubic feet, merch. 
Board feet 



Log rule 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 



Scribner Dec. C. 
Mill tallies 

Mill tallies 
Mill tallies 
Scribner Dec. C. 
Scribner Dec. C. 
Tiemann 
Tiemann 

Scribner Dec. C. 
Scribner Dec. C. 

Scribner Dec. C. 
Scribner Dec. C. 



Scribner Dec. C. 
Scribner 
Scribner Dec. C. 

Scribner Dec. C. 
Scribner Dec. C. 

Scribner 
Scribner 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 



Mill tallies 
Mill tallies 
Scribner 

Scribner Dec. C. 
Scribner Dec. C. 

Scribner Dec. C. 



TABLES USED IN FOREST MENSURATION 



513 



-Continued 



Conifers — Continued 



D.B.H. 


Height. 


Top 
diameter. 


Basis. ^ ^ 
Date 


Publication 


U. S. F. S. 
designation 


(Inches) 


(Feet) 


finches) 


Trees 




12-42 


80-160 


7.3-10.8 


1388 1907 


Bui. 36, U. S. Forest Service 


L7-V2 


12-42 


3-8 log 


7.3-10.8 


1394 1907 




L7-V4 


8-40 


1-9 log 




233 1914 


Manual for Timber Reconnaissance, 
Dist. 1, U, S. Forest Service 




2-20 


20- 80 




658 1920 


Bui. 820, U. S. Dept. Agr. 




4-20 


20- 80 


3 


615 1920 


" 




8-20 


20- 80 


5.5 


288 1920 


" 




8-20 


1-4 log 


5.5 


288 1920 


" 




14-54 


40-130 
15- 80 


6-16.4 
U 


413 1907 
372 1914 




P7-V1 


3-20 


Bui. 11, U. S. Dept. Agr. 




3-20 


15- 80 


U 


372 1914 






7-20 


40- 80 


5.5 


372 1914 






4- 8 


30- 70 


2.5 


Tapers 1914 






6-30 


20-120 


3-5 


1915 


Bui. 24, N. Car. Geol. Survey 




7-22 


40-120 


5 11 


.... 1915 




P76-V24 


14-36 


90-140 


7-15 


1915 




P76-V28 


8-22 


40-120 


5-11 


.... 1915 




P76-V23 


14-36 


90-140 


7-15 


1915 


" 


P76-V27 


7-22 


40-120 


5-11 


.... 1915 


" 


P76-V21 


14 36 


90-140 


7-15 


1915 


" 


P76-V25 


3-20 


30-100 


2 -3 


1915 


Bui. 234, U. S. Dept. Agr. 




7-24 


1-5 log 


6 


555 1915 






10 + 


1-5 log 


6.2-6.6 


1808 1915 






4-22 


30- 90 




644 1907 


Circ. 126, U. S. Forest Service 




10-24 


50-100 


6 


1817 1907 


" 




7-22 


h-^i log 
30- 70 
0-6 log 


6 

3-4 

9 


549 1913 

255 1913 

2000 .... 




P0-V13 






P0-V14 


8-18 




P0^V12 


9-18 


i-S^ log 
^5 log 
40-120 


8 

8 

6-18 


.... 1913 

1971 1915 

614 1904 




PO-VU 


8-25 




PO-V28 


7-36 


Bui. 36, U. S. Forest Service 




5-20 


40-100 




303 1914 


Bui. 139, U. S. Dept. Agr. 




8-34 


30-120 


6 


4282 1914 


* ' 




8-34 


1-7 log 


6 


4282 1914 


' ' 




7-30 


40-120 
60-100 


6 


613 1905 
259 1909 




P31-V11 


7-18 


Bui. 36, U. S. Forest Service 




10-27 


70-100 




964 1909 


' ' 




2-12 


10- 75 




228 1911 


Bui. 94, U. S. Forest Service 




4r-12 


30- 75 




228 1911 






2-12 


20- 70 




228 1905 


Bui. 36, U. S. Forest Service 




6-20 


40- 90 


6-8 


317 1915 


Bui. 308, U. S. Dept. Agr. 




6-20 


40- 90 


6-8 


317 1915 


" 




8-34 


40-120 


6-13 


3206 1915 






8-34 


U-6 log 


6-13 


3206 1915 


" 




10-80 


40-220 


8-16 


910 1917 


Bui 426, U. S. Dept. Agr. 




10-80 


1-12 log 


8-16 


910 1917 






10-80 


60-240 
30-120 


8-16 
5 


773 1913 
1578 1905 




P3-V13 


5-20 


Bui. 13, U. S. Dept. Agr. 




5-25 


30- 90 


4 


2000 1908 






5-27 


30- 90 


4 


2000 1908 






5-26 


30-120 


5 


1578 ! 1905 


" and Bui. 820, U. S. Dept. Agr. 




5-27 


30- 90 


4 


2000 1 1908 


Bui. 13, U. S. Dept. Agr. 




8-40 


40-140 


6-14 


3899 1910 






8-42 


40-110 
n-7 log 


6 
6 


1834 1913 
1834 1913 




P32-V40 


8-42 





P32-V39 


5-26 


30-120 
40- 90 


! I 


1578 1905 
260 ' 1913 




P32-V25 


8-20 





P32-V42 









514 



APPENDIX C 



TABLE LXXXVII 



Conifers — Continued 



Species 



Locality 



Tree class 



Unit of measure- 
ment 



Log rule 



Pine, white S. Appalachians 



Under 75 yrs. 



Pine, western white . 
Pine, western white . 
Pine, western white . 

Pine, western white 
Pine, western yellow 
Pine, western yellow- 
Pine, western yellow 
Pine, western yellow 
Pine, western yellow 
Pine, western yellow 
Pine, western yellow 
Pine, western yellow- 
Pine, western yellow- 
Pine, western yellow- 
Pine, western yellow- 
Pine, western yellow 
Pine, western yellow 
Pine, western yellow! 
Pine, western yellow 
Pine, western yellow- 
Redwood 

Redwood 

Redwood 

Spruce, black 

Spruce, black 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, red 

Spruce, Englemann. 

Spruce, Englemann, 
Spruce, Englemann, 
Spruce, Englemann, 
Spruce, Englemann, 

Spruce, white 

Spruce, white 

Tamarack 



Idaho 
Idaho 
Idaho 

Idaho 

Black Hills, S. Dak, 

California 

Black Hills, S. Dak, 

Klamath, Ore. 

Blue Mts., Ore. 

Arizona 

Arizona 

Arizona 

Arizona 

California 

S. Dakota, Idaho 

Montana 

Montana 

Montana 

Montana 

Colorado 

California 

California 

California 

Quebec 

Quebec 

Maine 

New Hampshire 

New Hampshire 

New Hampshire 

New Hampshire 

New York 

West Virginia 

New York 

New York 

Maine 

Maine 

Maine 

Maine 

New Hampshire 

New Hampshire 

New Hampshire 

New Hampshire 

New York 

New York 

West Virginia 

West Virginia 

Colorado, Utah 

Colorado, Utah 
Colorado, Utah 
Colorado, Utah 
Idaho, Montana 

Quebec 
Quebec 
Minnesota 



Sprouts 
Sprouts 
Original 



Old field 
Old field 
Original 
Original 
Original 
Original 
Original 
Original 



Board feet 
Board feet 
Board feet 
Board feet 

Cubic feet 
Cubic feet, total 
Cubic feet, total 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cu. ft., total O.B. 
Board feet 
Board feet 
Cubic feet 
Board feet 
Cubic feet, merch. 
Cubic ft. total O.B. 
Cu. ft., merch. O.B. 
Cu. ft., merch. O.B. 
Cubic feet, peeled 
Cu. ft., merch. O.B. 
Cu. ft., merch. O.B. 
Standards 
Standards 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Board feet 
Cubic feet, merch. 

peeled 
Board feet 
Board feet 
Board feet 
Board feet 

Cubic feet, merch. 
Board feet 
Cubic feet, total 



Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner DeX;. C. 



Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 
Scribner 



Dec. C. 
Dec. C. 
Dec. C. 
Deo. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 
Dec. C. 



Scribner Dec. C. 
Spaulding 



Quebec 



Dimick 
Dimick 
Maine 
Maine 

Scribner Dec. C 
Scribner Dec. C. 
New Hampshire 
New Hampshire 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 
Scribner Dec. C. 



Scribner Dec. C. 
Scribner Dec. 0. 
Scribner 
Scribner Dec. C. 



Quebec 



TABLES USED IN FOREST MENSURATION 



515 



-Continued 









CONIFERS- 


—Continued 




Diam- 
eter. 


Height. 


Top 
diameter. 


Basis. 


Date 


Publication 


U. S. F. S. 
designation 


(Inches) 


(Feet) 


(Inches) 


Trees 






8-20 


li-3i log 


6 


260 


1913 




P32-V41 


8-36 


30- 160 


6-8 


1791 


1908 


Bui. 36, U. S. Forest Service 


P2-V3 


8-36 


2-10 log 


6-8 


1791 


1908 




P2-V4 


8-60 


1-9 log 




306 


1914 


Manual of Timber Reconnaissance, 
Dist. 1, U. S. Forest Service 




8-44 


80-190 




1790 


1914 


Bui. 36, U. S. Forest Service 


P2-V5 


8-25 


30- 90 




1004 


1908 


Giro. 127, U. S. Forest Service 




12-48 


50-160 




710 


1908 


" 




8-25 


40-100 
2- 8i log 


6-14 


1419 
823 


1910 
1917 




P4-V31 


12-50 


Bui. 418, U. S. Dept. Agr. 




10-42 


2-8i log 


6-16 


1536 


1917 






10-50 


30-150 
1-8 log 


8 
8 


6099 
6099 






P4- V43 


10-50 




P4-V41 


12-40 


40-120 


8.3-17 


1822 


1911 


Bui. 101, U. S. Forest Service 




12-40 


1-6 log 


8.3-17 


1822 


1911 


" 




12-70 


60-220 
2-10 log 
1-8 log 
30-140 
U-8 log 
30-140 
l-6i log 


8-14 

8 
6-10 
6-10 

6-18 
6.1-10.6 


2396 
1193 
427 
427 
2822 
2438 
2167 


1911 
1913 
1913 
1913 
1916 
1916 
1916 




P4-V39 


12-50 




P4- V42 


10-40 




P4 V5 


10-40 




P4-V36 


8-40 




P4-V37 


8-40 




P4-V38 


12-43 




P4-V61 


6-24 


30- 90 
30- 90 
55-180 


6-7 


883 
763 
503 


1900 
1900 
1917 




R1-V3 


7-24 




R1-V2 


20-112 


Timberman, Dec, 1917, p. 38 




7-20 


46- 89 


4 


317 


1911 


For. Quar., Vol. IX, p. 591 




6-20 


13- 84 


4 


317 


1911 






6-25 


40- 90 


4.5 


246 


1920 


Bui. 544, U. S. Dept. Agr. 




6-14 


40- 70 




711 


1920 


' ' 




6-18 


40- 80 


5 


711 


1920 


' ' 




5-28 


40- 90 


4 


1226 


1920 


' ' 




6-14 


40- 70 


4-6 


711 


1920 


' ' 




6-26 


30-100 


4.5 


1591 


1920 






6-34 


50-100 


4.5 


417 


1920 


" 




8-26 


1-5 log 


6 


1507 


1920 






8-26 


30-100 


6 


1507 


1920 


" 




7-25 


40- 90 


6 


241 


1920 






7-25 


1-4 J log 


6 


241 


1920 


" 




7-25 


40- 90 


6-9 


241 


1920 






7-25 


1-5 log 


6-9 


241 


1920 






8-26 


30- 80 


6 


668 


1920 






8-26 


1-4 log 


6 


668 


1920 


" 




8-26 


30- 80 


6 


668 


1920 






8-26 


1-4 log 


6 


668 


1920 


' ' 




8-26 


30-100 


6 


1507 


1920 






8-26 


1-5 log 


6 


1507 


1920 


' ' 




8-34 


50-110 


6 


416 


1920 






8-34 


l§-6 log 


6 


416 


1920 


" 




7-36 


40-120 


6-8 


676 


1910 


Circ. 170, U. S. Forest Service 


S2-V4 


8-30 


40-120 


6-8 


676 


1910 


.. 


S2-V1 


8-30 


1-6 log 


6-8 


671 


1910 


" 


S2-V5 


7-26 


35-115 
1-9 log 


6 


2380 
189 


1915 
1914 




S2-V10 


8-40 


Manual for Timber Reconnaissance, 














Dist. 1, U. S. Forest Service 




7-25 


51-100 


4 


441 


1911 


For. Quart., Vol. IX, p. 590 




6-25 


44-112 


4 


1351 


1911 


p. 592 




7-15 


60-100 




246 


1905 




I-35-V4 











516 



APPENDIX C 















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520 



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APPENDIX D 

BIBLIOGRAPHY 

List of the most important works dealing with Forest Mensuration, in English: 
Carter, P. J. Mensuration of Timber and Timber Crops. Calcutta, Ind., 1893. 
Gary, A. Manual for Northern Woodsmen. Harvard University, Cambridge, 

1918. 
Cook, H. O. Forest Mensuration of the White Pine in Massachusetts. Boston, 

1908. Office of State Forester. 
D'Arcy, W. E. Preparation of Forest Working Plans in India. Calcutta, 1898. 
Graves, H. S. Forest Mensuration, John Wiley & Sons. New York, 1908. 
Graves, H. S. • Woodsman's Handbook. Bui. 36, U. S. Forest Service, 1910. 
Mattoon, W. R., and Barrows, W. B. Measuring and Marketing Woodlot 

Products. Farmers' Bui. 715, U. S. Dept. Agr., 1916. 
McGregor, J. L. L. Organization and Valuation of Forests. London, 1883. 
Mlodziansky, a. K. Measuring the Forest Crop. Bui. No. 20, Div. of Forestry, 

U. S. Dept. Agr., 1898. 
PiNCHOT, Gifi^ord. The Adirondack Spruce. New York, 1898. 
PiNCHOT, G., and Graves, H. S. The White Pine. New York, 1896. 
ScHENCK, C. A. Forest Mensuration. Sewanee, Tenn., 1905. 
ScHLicH, Wm. Manual of Forestry, Vol. III. London, 1911. 
\^''iNKENWERDER, H. Manual of Exercises in Forest Mensuration. John Wiley 

&Sons. New York, 1921. 

List of the most important works dealing with Forest Mensuration, in German. 
Selected from bibliography published in "Forest Mensuration," by H. S. Graves, 
with some additions : 

Special Works on Forest Mensuration 

Baur, Franz. Die Holzmesskunde. Berlin, 4th ed., 1891. 

Brehmann, Karl. Anleitung zur Aufnahme der Holzmasse. Berlin, 1857. 

Anleitung zur Holzmesskunst. Berlin, 1868. 

Fankhauser, F. Praktische Anleitung zur Holzmassen-Aufnahme, 3d edition, 
Bern, 1909. 

Heyer, Gust. Ueber die Ermittelungen der Masse, des Alters und des Zuwachses 
der Holzbestiinde. Dessau, 1852. 

Heyer, Karl. Anleitung zu forststatischen Untersuchungen. Giessen, 1846. 

Klauprecht. Die Holzmesskunst. Karlsruhe, 1842 and 1846. 

Konig, G. Die Forst-Mathematik mit Anweisung zur Forstvermessung. Gotha, 
1835. Revised by Dr. Grebe, 1864. 

Kunze, M. F. Lehrbuch der Holzmesskunst. Berlin, 1873. 

Langenbacher, Ferd. Forstmathematik. Berlin, 1875. 

Lamgenbacher, F. L., und Nossek, E. A. Lehr- und Handbuch der Holzmess- 
kunde. Leipzig, 1889. 

MtJLLER, Udo. Lehrbuch der Holzmesskunde. Leipzig, 2d edition, 1915. 

ScHWAPPACH, Adam. Leitfaden der Holzmesskunde. Berlin, 1903. 

521 



522 APPENDIX D 

Smalian, L. Beitrag zur Holzmesskunst . Stralsund, 1837. 

Anleitung zur Untersuchung des Waldzustandes. Berlin, 1840. 

Statz, Paul. Die Abstandszahl, ihre Bedeutung fur die Forsttaxation, Bestandes- 

erziehung und Bestandespflege, Freiburg, 1909. 
Tkachenko, M. Das Gesetz des Inhalts der Baumstamme una seine Bedeutung 

fiir die Massen- und Sortimentstafeln. Berlin, 1912. 

Works on Forest Management Containing Chapters on Forest 

Mensuration 

Borggreve, B. Die Forstabschatzung. Berlin, 1888. 

VON FiscHBACH, C. Lehrbuch der Forstwissenschaft. Berlin, 1886. 

Graner, F. Die Forstbetriebseinrichtung. Tiibingen, 1889. 

VON Guttenberg, a. F. Forstbetriebsienrichtung. Wien and Leipzig, 1903. 

Hess, R. Encyclopedic und Methodologie der Forstwissenschaft. Nordlingen, 

1885. 
Heyer, Gust. Waldertragsregelung. Leipzig, 1893. 
JuDEicH, F. Die Forsteinrichtung. Dresden, 1893. 

LoREY, TuisKO. Handbuch der Forstwissenschaft. 3d edition, Tubingen, 1913. 
Stotzer, H. Die Forsteinrichtung. Frankfurt, 1898. 
Weber, Rudolf. Lehrbuch der Forsteinrichtung. Berlin, 1891. 
Weise, W. Ertragsregelung. Berlin, 1904. 

List of the most important works dealing with Forest Mensuration, in French. 
From bibliography published in "Studies of French Forestry," by T. S. Woolsey, Jr.: 

L'amenagement des forets (2d Edit.). Puton. Paris, 1874. 

Notice sur les dunes de la Coubre. Vasselot de Regne. Paris, 1878. 

Amenagement des forets-Estimation. Fallotte. Carcassonne, 1879. 

La methode du controle de Gurnaud. Grandjean. Paris, 1885. 

L'art forestier et le controle. Gurnaud. Besangon, 1887. 

L'amenagement des forets (V. Edit.). Tassy. Paris, 1887. 

Traite d'economie forestiere. Puton. Paris, 1888. 

Cours d'amenagement professe a I'Ecole forestiere (1885-1886) 2 cahiers. Reuss. 

Nancy, 1888. 
Diagrammes et calculs d'accroissement. Bartet. Nancy, 1889. 
Guide theorique et pratique de cubage des bois. Frochot. Paris, 1890. 
La methode du controle d I'Exposition de 1889. Gurnaud. Pans, 1890. 
Note sur une nouvelle methode forestiere dite du controle de Gurnaud. de Blonay. 

Lausanne, 1890. 
Traite d'economie forestiere. Amenagement. Puton. Paris, 1891. 
Le traitement des bois en France. Broillard. Paris, 1894. 
Estimations et exploitabilites forestieres. Bizot de Jontenz. Gray, 1894. 
Notes pour la vente et Tachat des forets. Galmiche. BesanQon, 1897. 
Notes forestieres— Cubage, estimation, etc. Devarenne. Chaumont, 1889. 
Economic forestiere. Huff el. Paris, 1904-07. 
Cubage des bois sur pied et abattus manuel pratique. Berger, Levrault et al. Paris, 

1905. 
Mathematiques et Nature. Broillard. Besangon, 1906. 
Aide memo ire du forestier-Sylviculture. Demorlaine. Besangon, 1907. 



INDEX 



PAGE 

Abney clinometer 239 

Abnormal cross sections 17 

plots, rejection, yield tables 404 

Absolute form factors 212 

quotient 207 

versus relative accuracy in mensuration 3 

Accuracy in timber estimating, limits of 301 

of results in timber estimating, choice of system for 261 

of timber estimates, methods of improving 288 

of volume tables, checking 189 

of yield predictions 412 

Accurate formula log rules 65 

log rules, need for 50 

Acre, area of 6 

Actual density of stocking, determination of 413 

estimate or measurement of the dimensions of every tree of merchant- 
able size 257 

Adirondack standard or market 28 

Adoption of a standard log length for volume tables 182 

Advantages of graphic plotting of data 106 

Age, as affected by suppression 341 

average, definition and determination 337 

classes, group form, separation 418 

in yield tables 397 

economic 341 

from annual whorls 337 

groups, yield tables for 412 

in even-aged versus many-aged stands, the factor of 325 

of average trees and of stand, determining 339 

of seedling 336 

of stand, determining 335, 339 

of stands relation to volume 449 

of timber, effect on methods of estimating 265 

of trees, determining 335 

separation of, in yields 416 

Ake log rule 36 

Annual increment of many-aged stands 390 

whorls of branches as an indication of age 337 

Applicabihty of Hoejer's formula in determining tree forms 210 

523 



524 INDEX 

PAGE 

Application of graphic method in constructing volume tables 169 

of yield tables in predicting yields 322 

Appolonian paraboloid 19 

Appraisal, timber as distinguished from forest survey 269 

Arbitrary standards in constructing log rules 49 

Area determination, importance in timber estimating 267 

for age groups on basis of diameter groups 422 

for two age groups on basis of average age 419 

of plots in yield tables 397 

separation of in yields 416 

units, size, relation to per cent of area to be estimated 262 

Areas determined from density factor 416 

of circles, table LXXVIII 490 

of cross sections 17 

of crowns 423 

of different types, separation, method 290 

of immature timber, growth on 451 

separation of, effect on density 453 

Arkansas, statute log rule 68 

Average age, basis for determining volume and area of two age groups 419 

definition and determination 337 

Average board-foot volume, tree containing 311 

diameter growth, determination 346 

heights of timber and site classes 291 

heights of trees based on diameter 258 

log method of estimating 143 

stand per acre from partial estimate 260 

trees, age, determining 339 

trees, volume and diameter, determination of 338 

Averages employed in timber estimating, six classes of 258 

Ballon log rule 75 

Barbow cruising compass 248 

Bark as a waste produ(!t 13 

as affecting diameter in volume tables 150 

marks, log 99 

measurement in cords 134 

volume of 163 

width, measurement for volume 161 

Basal area, definition 7 

areas, table LXXVIII 490 

use in predicting yields 415 

Base line 281 

Basis for board-foot volume tables 182 

for cordwood converting factors , 127 

of determining dimensions of the frustum 219 

Baughman log rules 72 

Bangor log rule 85 

Baur's method of constructing yield tables 396 

Baxter log rule 67 



INDEX 525 

PAGE 

Beaumont log rule 85 

Big Sandy Cube rule 33 

Billets, definition 14 

measurement 122 

products made from 14 

Biltmore pachymeter 248 

stick 230 

errors in use of 232 

Table XXXVIII 232 

graduation 233 

Table XXXIX 233 

Blank areas, separation in estimating 289 

Blodgett foot 30 

or New Hampshire log rule 30 

Board-feet, basis of application to standing timber 139 

errors in use of cubic rules for 42 

frustum form factors for merchantable contents in 218 

log rules expressed in, but based directly upon cubic contents 34 

merchantable form factors for 225 

volume tables for 182 

Board-foot contents, construction of log rules for 58 

middle diameter as a basis for 46 

of logs 40 

rules of thumb 252 

converting factors for various piece products. Table LXXVI 478 

log rules, limitations to conversion of 83 

necessity for 40 

rules, formula based on cubic contents 35 

volume tables, construction of 188 

volume, tree containing average 311 

measure, definition 8 

log scaling for 88 

Bole, in volume tables 158 

Bolts, definition 14 

measurement 122 

products made from ^ 14 

Borer, increment 358 

Boundaries, determination in timber estimating 267 

Boynton log rule 85 

Branch wood or lapwood in volume tables 177 

Breakage 116 

Breast-high form factors 212 

, Table LXXXII 497 

Breymann's formula 22 

British Columbia log rule 64 

Brubaker log rule 85 

Brush, effect on width of strips 275 

Bulk products, forms of 11 

Business, definition 2 

Butt rot 110 



526 INDEX 

PAGE 

Calcasieu log rule 36 

Calculation of true frustum form factor 221 

of volumes of frustums 221 

California log rule 75 

Caliper scale 97 

definition 23 

Calipers, description and method of use 227 

Canada, Dominion forestry branch, log rule 73 

Canadian log rules 76 

Carey log rule 66 

Cat faces 115 

Cedar, western red, poles 469 

white, poles 467 

Center rot 108 

Chain, unit of measurement, definition 6 

Champlain log rule 65 

Chandler, B. A 220 

Chapin log rule 85 

Character and utility of frustum form factors 219 

of crown tree for volume tables 157 

of growth per cent 318 

Chart of growth studies 328 

Check estimating 308 

Checking the accuracy of volume tables 189 

Check scaUng. .' 117 

Checks, heart 112 

surface 115 

Chestnut oak, height growth, Milford, Pa., Table LVII 371 

volume growth, cubic, Table LVIII 376 

poles, minimum circumference, Table LXXII 472 

Choice of a board-foot log rule for a universal standard 84 

system for timber estimating with relation to accuracy of results .... 261 

of units in timber estimating 140 

Christen hypsometer 243 

Circular plots, sizes. Table XLII 286 

Classification and averaging of tree volumes according to diameter and height 

classes 163 

of tree, measurements required in volume tables 156 

of trees by diameter 151 

height in volume tables 151 

Clement's log rule 66 

Click's log rule 66 

CUnometer, Abney 239 

Codominant tree, definition 158 

Columbia River Log Scaling and Grading Bureau log grades 460 

Combination log rules 76 

volume tables for two or more products 193 

Common grades of lumber 457 

Comparison of growth for diameter classes 360 

of log rules based on cubic contents, Table II 37 



INDEX 527 

PAGE 

Comparison of log rules based on diameter at middle and at small end of log . . 26 

on formulae 61 

of scaled and cubic contents by different log rules 36 

Compass, hand 276 

staff 277 

Composition of stands as to species, effect on yield 393 

Computation of volume of the tree 161 

Cone 19 

Connecticut River log rule 68 

Constantine log rule 34 

Construction and use of local volume tables 174 

of board-foot volume tables 188 

of a log rule, standardization of variables in 49 

of log rules based on diagrams 72 

mathematical formulae 59 

for board-foot contents 58 

for mill talUes 78 

of standard volume tables for total cubic contents 154 

of volume table from frustum form factors 224 

of yield table with site classes based directly on yields per acre . . . 406 

on height growth 401 

based on crown space, for many-aged stands 422 

tables, Baur's method 396 

Contents of standing trees, rules of thumb for estimating 251 

solid, of logs, formulae 20 

Conversion of board-foot log rules, limitations to 83 

of International rule j-inch saw kerf for other widths of kerf, Table 

XIII 81 

of log rules with J-inch saw kerf to other widths of kerf. Table XIV . . 82 
of values of a standard rule to apply to different widths of saw kerf 

and thickness of lumber 80 

of volume tables for cubic foot, to cords 180 

Converter poles 473 

Converting factors, cordwood basis for 127 

for cordwood. Table XX 129 

for log rules 27 

for sticks of different diameters 129 

lengths 128 

piece products to board-feet 478 

standard cordwood 128 

stacked cords to board-feet, factors for 135 

Cook log rule 35 

Coordination of merchantable heights with top diameters 184 

Cord foot 123 

, long 121 

measure 121 

definition 7 

discounting for defects in 133 

Cords, conversion of volume tables from cubic feet to 180 

Cord, short 121 



528 INDEX 

PAGE 

Cord, standard, definition 7 

versus short cords and long cords 121 

volume tables for 177 

to board-feet, factors for converting 135 

Cordwood converting factors, basis for 127 

standard 128 

log rules 132 

methods of measurement 123 

rule, Humphrey caliper 132 

weight as a measure of 137 

Correction factors for volume, use of 293 

of average stand per acre 260 

Cost of estimating timber 302 

Count, and average tree in estimating 259 

and partial tally of trees in estimating 259 

Cracks, frost 1 12 

Crook or sweep, deductions for. Table XVIII 116 

in scaling 116 

waste from 51 

Crooked River log rule 35 

Cross sections, abnormal 18 

diameters and areas 17 

Cross ties 474 

volume tables for 191 

Crown class and suppression as affecting height growth 366 

definition 157 

effect on diameter growth 353 

cover, density of 424 

of tree, character for volume tables 157 

space, yield tables based on, for many-aged stands 422 

spread of loblolly pine, Ala., Table LXI 389 

Crowns, areas of 423 

width of, measurement 423 

Cruisers' method, Lake States estimating 283 

methods. Southern estimating 283 

Cuban One Fifth log rule 34 

Cube Rule, Big Sandy 33 

Cubic and board foot contents of logs compared. Table III 41 

contents of cylinders, Table LXXVII 480 

scaled by various log rules, Table II 37 

log rules based directly upon, but expressed in board-feet 34 

on 26 

of logs, measurement 16 

scaled as board feet, by different log rules, comparison . . 36 

of squared timbers, log rules for . 33 

of stacked wood, soUd 124 

rules of thumb 251 

total, construction of standard volume tables for 154 

weight as a basis of measuring 33 

foot, use of, in log scaling 31 



INDEX 529 

PAGE 

Cubic measure, definition 8 

in log measurements 28 

relation to true board-foot log rules 39 

stacked, definition 7 

measure as a substitute for 121 

meter in log measurement 28 

rules for board-feet, errors in use of 42 

volume, log rules based on 28 

merchantable, standard volume tables 177 

Cull factor, or deductions for defects in timber estimating 271 

in log scaling, relation to grades of timber 458 

in volume tables 179 

Cumberland River log rule 35 

Current annual growth 315 

growth, compared with yield tables and mean annual growth 445 

loblolly pine, diameter, Table LVI 363 

per cent 429 

permanent sample plots for measurement of 443 

spruce, Adirondacks, Table LIV 360 

use of yield tables in predicting 436 

height growth 371 

periodic growth based on diameter classes 358 

or periodic growth of stands, measurement 436 

Curves, harmonized, for volumes based on height 170 

for standard volume tables based on diameter 169 

for taper tables, based on D. B. H 200 

on total heights of tree 202 

original based on height above stump 197 

Cut-over areas, application of yield tables ba-sed on age to 441 

growth on 438 

Cylinder 19 

as the standard of scaling 90 

d'Aboville method for determining form quotients 248 

Data required from forest survey for growth 447 

which should accompany a volume table 188 

D. B. H., correlation with stump growth 348 

definition 150 

merchantable limit at 177 

Decades, method of coimting 343 

Decimal C, Scribner log rule 74 

rule, Scribner 73 

values below 12 inches, Scribner log rule. Table XII 74 

Deducting a per cent of total scale 107 

Deductions by sectors 115 

by slabs 114 

for crook or sweep. Table XVIII 116 

for defects in timber estimating 271 

from scale for unsound defects 105 

from sound scale versus over-run 90 



530 INDEX 

PAGE 

Defect, effect upon grades of logs 460 

Defective logs, merchantable 99 

scaling of 105 

trees, measurement for volume tables 183 

Defects, deductions for, in timber estimating 271 

exterior 113 

in cord measure, discounting for 133 

in lumber 456 

interior 108 

or cull in volume tables 179 

sound and unsound 103 

unsound, deductions from scale for 105 

Degree of uniformity of stand as affecting methods employed in estimating. . . . 265 

Dendrometers 247 

Density factor, determination of areas from 416 

factors, application in prediction of growth from yield tables 414 

for mature stands, effect of separation of areas of immature 

timber 453 

of crown area 424 

of stand, effect on diameter growth 352 

of stocking as aiTecting growth and yields 392 

of stocking, empirical 413 

of stocking, standard for normal 397 

Derby log rule ' 36 

Derivation of local volume table from standard volume tables 175 

of standard breast-high form factors 213 

Description of plot, yield tables 399 

Determination of what constitutes a merchantable log 99 

Determining the age of stands 335 

of trees 335 

Diagrams, construction of log rules based on 72 

in construction of log rules 58 

use of, for deductions in scaling 106 

Diameter alone, versus diameter and height as basis of volume tables 152 

and height classes, classification and averaging of tree volumes by ... . 163 

at middle of log, scahng practice based on 97 

at small end of log, scaling practice based on 91 

breast high 150 

in measuring standing trees 226 

Classes 227 

comparison of growth for 360 

current periodic growth based on 358 

clasification of trees by 151 

groups as basis of age groups 422 

growth, basis for determining 342 

computation of 346 

correction for seedUng age 348 

effect of species on 351 

in even-aged stands, laws of 354 

in many-aged sliands, laws of 357 



INDEX 531 

PAGE 

Diameter growth of trees growing in stands, factors influencing 351 

on sections, measurement of •. 342 

purpose of study 342 

relation to volume growth 374 

spruce, Table LI 345 

harmonized curves for volume based on 169 

in determination of log grades 459 

instruments for measuring 227 

of average trees, determining 338 

of log, relation to per cent of utilization in sawed lumber 40 

tape 229 

Diameters, abnormal 18 

and areas of cross sections 17 

bark as affecting, in volume tables 150 

measured at ends of log 22 

at middle of log 23 

point of measurement, in volume tables 148 

scaling 92 

Dimensions of frustum, basis, in form factors 219 

of stick, effect of, on solid contents of stacked wood 126 

of tree containing average board-foot volume 311 

Diminishing numbers, law of 318 

Direct ocular estimate of total volume in stand 256 

Discomiting for defects in cordwood measure 133 

Distances between strips in estimating 264 

Doyle-Baxter log rule 77 

Doyle log rule 68 

rule, errors in, effect upon scaling and over-run 70 

-Scribner log rule 76 

Dominant tree, definition 158 

Drew log rule 85 

Durability 466 

Dusenberry log rule 85 

Economic age of trees 34I 

Edgings, waste from 50 

Effect of dimensions of stick on solid contents of stacked wood 126 

of errors in Doyle rule upon scaling and over-run 70 

of irregular piling on solid contents of stacked wood 124 

of losses versus thimiings upon yields 324 

of minimum dimensions of merchantable boards upon deductions in scaling 107 

of seasoning on volume of stacked wood 123 

of variation in form of sticks on solid contents 125 

Empirical density of stocking 4I3 

yield tables 396 

use of 413 

English system of measurement 6 

Errors in Doyle rule, effect upon scaling and over-nm 70 

in use of Biltmore stick 232 

of cubic rules for board-feet 42 



532 INDEX 

PAGE 

Estimate, ocular, of total volume 256 

of every tree 257 

Estimates covering a part of the total area 273 

extensive 308 

total or 100 per cent 271 

Estimating a part of the timber as an average of the whole 257 

by means of felled sample trees 310 

by plots arbitrarily located 297 

contents of standing trees, rules of thumb 251 

log as the unit of 141 

quality of standing timber 297 

strip, systems in use 282 

timber, choice of units in 140 

cost 302 

tree as a unit in 144 

use of forest types in 288 

Estimation of standing timber, principles underlying the 255 

of tree dimensions, ocular. 234 

Evansville log rule 35 

Even-aged stands, laws of diameter growth 354 

normal yield tables for 395 

versus many-aged form of stands 388 

stands, definition 337 

Extensive estimates 308 

Extension, Scribner log rule 74 

Exterior defects 113 

Fabian's log rule 76 

Face, lumber 456 

Factors affecting the growth of stands 384 

determining the methods used in timber estimating 255 

width of strips 274 

for converting stacked cords to board-feet 135 

Factory or shop grades 457 

Faustmann hypsometer 240 

Favorite log rule 85 

Felled sample trees, methods of estimating 310 

Fence stays 473 

Fifth girth 25 

Finance, forest, relation to mensuration 3 

Finch and Apgar log rule 85 

Finished lumber grades 456 

Finishing grades 457 

Fixed or variable limits for top diameters 183 

Florida, statute log rule 68 

Forest cover, map 268 

finance, relation to mensuration 3 

growth determination for, coordination of forest survey 447 

management, relation to mensuration 3 

mensuration, definition 1 



INDEX 533 

PAGE 

Forest property, definition ' 1 

Service hypsometer 241 

standard valuation survey 282 

survey as distinguished from timber estimating 268 

coordination with growth determination for forest 447 

data required for growth 447 

definition 5 

surveying, as a part of the forest survey 270 

relation to mensuration 5 

survey, timber appraisal distinguished from 269 

total increment of, inclusive of immature stands 443 

.types, use in estimating 288 

valuation, relation to timber appraisal 269 

Forestry, relation to growth measurements 2 

Forests composed of all age classes, growth per cent of 434 

having a group form of age classes 418 

Form as a third factor affecting volume 196 

class, determination from form point. Table XL 250 

classes and form factors 205 

and universal volume tables as applied to conditions in America. . 215 

based on form quotient 206 

factor, Riniker's absolute 212 

factors 211 

absolute 212 

breast-high 212 

for board-feet 225 

frustum, character and utility 219 

merchantable 214 

normal 212 

standard breast-high 213 

height 215 

of logs, the 18 

of red pine 210 

of stands 388 

of sticks, effect on solid cubic contents 125 

of trees and taper tables 196 

Hoejer's formula for 209 

of white pine 210 

point method of determining form classes, Jonson 249 

position of, to determine form class; Table XL 250 

quotient, absolute 207 

as the basis of form classes 206 

quotients, d'Aboville method for determining 248 

of trees, wind pressure 208 

relation to volume and diameter growth 374 

Formula for board-foot rules based on cubic contents 35 

for tree form, Hoejer's 209 

Huber's 20-21 

log rules 65 

log rules, inaccurately constructed 67 



534 INDEX 

PAGE 

Formula, Newton's 21 

prismoidal 21 

Schiffel's, derivation 206 

use in computing volume of tree 163 

Smalian's 20-21 

Formulae, general, for all log rules 77 

in construction of log rules 58 

waste from saw kerf 53 

Forties, unit of estimating 263 

Forty, definition 6 

Forty- five log rule 85 

Frost cracks 112 

Frustum, basis of determining dimensions of, in frustum form factors 219 

form factor, principle of 278 

true, calculation of the 221 

factors, character and utility 219 

construction of volume table from 224 

for merchantable contents in board-feet 218 

Frustums 20 

volume, calculation 221 

Full and scant thicknesses of boards as aflfecting over-run 49 

General formula? for all log rules 77 

Girth as a substitute for diameter in log measurements 24 

Glens Falls standard 28 

Goble log rule 33 

Graded log rules 78 

applied to the log, in estimating 299 

tables 195 

volume tables 193 

applied to tree in estimating 299 

Grades, finishing 457 

of lumber 455 

and log grades 103 

in estimating, method based on sample plots and log tables . 300 

in standing timber 298 

relation to cull in log scaling 458 

log 103 

Grading rules. Southern yellow pine 457 

Graduation of Biltmore stick, Table XXXIX 233 

Graphic method, application in constructing volume tables 169 

of determining diameter growth. .' 347 

plotting of data; its advantages 166 

Graves, H. S. Method of stem analysis 382 

Ground rot 110 

Group form of age classes, separation of areas 418 

Growth and yields, density of stocking as affecting 392 

by diameter classes, projection 361 

correlation of stump with D. B. H 269 

current annual 315 



INDEX 535 

PACK 

Growth current periodic, leased on diameter classes 358 

data, relative utility of different classes of 327 

determination for forest, co-ordination of forest survey with 447 

diameter, purposes of study 342 

effect of treatment on 391 

for diameter classes, comparison of 360 

increased, method of determination 363 

loblolly pine, old field, diameter; Table LIII 350 

mean annual 315 

of stands after cutting, increased 438 

reduced 439 

• current or periodic, measurement 436 

factors, affecting 384 

prediction by growth per cent 432 

of trees as basis for method of predicting current growth of stands 436 

in diameter 342 

in height 365 

in volume 374 

on areas of immature timber 450 

on even-aged stands, in large age groups 412 

per cent 316 

character 318 

definition 429 

determination 429 

in forests composed of all age classes 434 

in quality and value 435 

to determine growth of stands by comparison with measured 

plots 433 

use to predict growth of stands 432 

periodic 315 

annual 315 

prediction by projecting past growth of trees 323 

short leaf pine, diameter, La., Table LV 362 

studies, chart of 328 

purpose and character 315 

volume for single trees, computation 289 

substitution of tapers for 379 

Hand compass, use in strip surveys 276 

Hanna log rule 75 

Harmonized curves for standard volume tables based on diameter 169 

for volume, based on height 170 

Heart checks 112 

Height classes, tree volumes averaged by 163 

classification of trees by, in volume tables 151 

growth a basis for site qualities 386 

basis for site classes in construction of yield table 401 

chestnut oak, Milford, Pa., Table LVH 371 

current 371 

influences affecting 365 



536 INDEX 

PAGE 

Heiglit, growth of trees in 365 

, measurement 368 

relations to diameter growth 367 

substitution of curves of height on diameter 371 

harmonized curves for volume based on 170 

of seedlings, western yellow pine, Table L 336 

of stump 156 

total measurement 156 

Heights, measurement of 235 

measuring, technique 245 

of timber, average, and site classes 291 

total versus merchantable 184 

Herring log rule 85 

Hewn ties 474 

Heyer's method, xylometric for cordwood 132 

Hoejer's formula for tree form 209 

Holland log rule 76 

Hop poles 473 

Hoppus, or Quarter Ciirth log rule 25 

rule 34 

Horseshoe method of estimating 284 

Hossfeld's formula 22 

Huber's formula 20 

in measuring branch wood 177 

use in computing volume of tree 162 

Humphrey caliper cordwood rule 132 

Hybrid log rules 76 

Hypsometer, Christen 243 

Faustmann 240 

Forest Service 241 

Klaiissner 236 

Merritt 238 

Weise 240 

Winkler 241 

Hypso meters 235 

based on the pendulum or plumb-bob 239 

Idaho, statute log rule 73 

Immature stands, increment of, as part of total increment of forest 443 

timber, growth on 450 

Importance of area determination in timber estimating 267 

Increased growth of stands after cutting 438 

method of determination 363 

Increment borer 358 

use • 336 

Index yield tables 396 

Influence of log rule on deductions for defects 107 

Influences affecting height growth 365 

over-run, methods of manufacture 47 

the log rule itself 47 



INDEX 537 

PAGE 

Inscribed Square log rule 33 

Inspection and measurement of piece products 477 

Instruments for measuring diameter 227 

Interior defects 108 

Intermediate tree, definition 158 

International log rule for i-inch kerf, Table LXXX 493 

g-inch kerf log rule 63 

j-inch kerf log rule 64 

Introduction of taper into log rules 44 

Inventory of timber 268 

Isosceles triangles as basis of height measure 235 

Jack Pine, growth, Minnesota, Table XLVII 318 

Jonson form point method of determining form classes 249 

Tor 207 

Klaussncr hypsometer, principle of 235 

Knots, rot entering from 112 

Lagging 474 

Lake states, cruisers' method of strip estimating 283 

Lapwood, in volume tables 177 

Large timber on the Pacific Coast, methods of estimating 287 

Law of diminishing numbers as affecting growth of trees and stands 318 

Laws of diameter growth in even-aged stands, based on age 354 

in many-aged stands, based on diameter 357 

Leaning trees, height, measurement 245 

Legal status of scaler 119 

Lehigh log rule 35 

Lengths, log 16 

scaling 91 

Licking River log rule 86 

Limitations of taper tables 204 

to conversion of board-foot log rules 83 

Limits of accuracy in timber estimating 301 

Loblolly pine crown spread, Ala., Table LX 389 

current growth, diameter, Table LVI 363 

old field, growth in diameter. Table LIII 350 

Local volume table, form, Table XXXI 175 

tables, definition 153 

derivation from standard tables 175 

construction and use 174 

Log as the imit of estimating 141 

brands 99 

grades 103 

defect, effect upon 460 

determination 459 

examples, hardwoods 460 

softwoods 460 

purpose 455 

length, standard for volume tables 182 



538 INDEX 

PAGE 

Log lengths 16 

merchantable, what constitutes a 99 

rule, Baxter 67 

British Columbia 64 

Blodgett or New Hampshire 30 

board-foot, choice of, for a universal standard 84 

Carey 66 

Champlain 65 

Clements' 66 

CUck's 66 

Doyle 68 

Doyle-Scribner 76 

for round edged lumber, Massachusetts 79 

influence on deductions for defects 107 

International i-inch kerf 63 

j-inch kerf 64 

McKenzie 63 

Maine 76 

New Brunswick 76 

New Hampshire or Blodgett 30 

Preston 66 

Quebec 76 

Scribner 73 

Scribner-Doyle 77 

Spaulding 75 

Tiemann 67 

Thomas' accurate 66 

Wilson 66 

based on cubic contents 26 

on diagrams, construction of 72 

on diameter at middle and at small end of log, comparison .... 26 

on formulae, comparison of 61 

on mathematical formula, construction of 59 

rules, Baughman 72 

board-foot, necessity for 40 

Canadian 76 

comparison of scaled cubic contents by different 36 

definition 8 

expressed in board-feet but based directly upon cubic contents 34 

for board-foot contents, construction of 58 

for cubic contents of squared timber 33 

formula, accurate 65 

from mill tallies, construction 78 

general formulae for all 77 

graded 78 

appUed to log, in estimating 299 

in use, based on cubic volume 28 

need for more accurate 50 

obsolete 36, 85 

taper, introduction of, into 44 



INDEX 539 

PAGE 

Log rules, true board-foot, relation to cubic measure 39 

run or average log method 143 

scale, the 88 

scaling, cull, relation to grades of lumber 458 

for board measure 88 

use of cubic foot in 31 

stamps 99 

tables, graded 195 

Logging conditions 269 

Logs, board-foot contents 40 

defective, scaling of 105 

measurement of cubic contents 16 

solid contents of, formulae 20 

technique of measuring 22 

the form of 18 

Long cord 122 

Losses of trees, correction for, in growth prediction 437' 

versus thinnings, effect upon yields 324 

Lot, area unit, definition 6 

Lumber, defects 456 

grades and log grades 455 

of 103 

Lumbering, relation to timber estimating 2 

Limberman's Favorite log rule 85 

log rule 35 

Lumber, thicknesses of, conversion of values of a standard rule to apply to 

different 80 

Maine log rule 76 

Management, forest, relation to mensuration 3 

Manufacture, the factor of waste in 13 

Manufactured products, forms of 11 

Many-aged form of stands 388 

stands, annual increment of 390 

application of yield table based on crown space to 425 

definition 337 

factor of age in 325 

laws of diameter growth 357 

yield tables based on crown space for 422 

Map, forest cover 268 

soil 268 

timber types 268 

topographic 268 

Market, cubic standard 28 

Massachusetts log rule for round-edged lumber 79 

Mathematical formulae, construction of log rules based on 59 

Mathematics, relation to mensuration 3 

McKenzie log rule 63 

Mean annual growth 315 

per cent 429 



540 INDEX 

PAGE 

Mean diameters, error in use of 23 

end formula, use in computing volume of tree 161 

sample tree method. 311 

Measurement of bark in cords 134 

of cordwood, methods of 123 

of current growth on permanent sample plots 443 

of defective trees for volume tables 183 

of diameter growth on sections 342 

of height by a straight stick held in hand 235 

growth 368 

of heights 235 

of log lengths 16 

of permanent sample plots 312 

of piece products 466 

of solid contents of stacked cords 132 

of stacked wood cut for special purposes 122 

of standing trees 226 

of tree diameters 227 

of upper diameters 247 

of waste 179 

of width of crowns 423 

systems used in forest mensuration 6 

Measurements of the tree required for classification in volume tables 156 

required for tree analyses 289 

on each plot, in yield tables 398 

to obtain the volume of the tree. Systems used 158 

Measuring and predicting the current or periodic growth of stands 436 

diameter, instruments for 227 

heights, technique of 245 

logs, technique of 22 

standing timber for volume 226 

stick for log lengths 16 

Medwiedew's method 387 

Mensuration, Forest, definition 1 

Merchantable boards, minimum dimensions, effect of, in making deductions in 

scaling 107 

Merchantable contents in board-feet, frustum form factors for 218 

cubic volume, standard volume tables 177 

form factors 214 

for board-feet 225 

heights as a basis for tree classes 184 

coordination with top diameters 184 

limit in tops and at D. B. H 177 

log, determination of 99 

versus used length 178 

Merritt hypsometer 238 

for merchantable heights 246 

Method of constructing taper tables 197 

of counting decades for growi.h 343 

of deducting sawdust first, construction of log rules 59 



INDEX 541 

PAGE 

Method of deducting slabs first, construction of log rules . . . ; 59 

of determining form classes, Jonson form point 249 

of graded log rules applied to the log 299 

volume tables applied to tree 299 

of mill-run applied to stand 299 

of running strip surveys 276 

of separating areas of different types 290 

of volume growth by use of tapers 379 

Methods of estimating dependent on use of plots arbitrarily located 297 

systematically spaced 285 

Pacific coast 284 

• plots, large timber on the Pacific coast 287 

spruce in Northeast 287 

strip, horseshoe 284 

Lake States timber cruisers 283 

southern timber cruisers 283 

valuation survey 282 

Yale Forest School 284 

which utilize types and site classes 292 

of height measurement based on similarity of isosceles triangles 235 

of right triangles 238 

of improving the accuracy of timber estimates 288 

of making deductions for defects 105 

of measurement of cordwood 123 

of scaling a log, effect of. Table V 45 

of timber estimating 267 

of training required to produce efficient timber cruisers 303 

used in constructing log rules for board-feet 58 

in timber estimating, factors determining the 255 

Metric system, conversion table. Table LXXIX 492 

of measurement 6 

Middle diameter as a basis for board-foot contents 46 

Mill factor, substitution for log rules, in universal tables 146 

grade or mill scale studies 461 

-run as basis of grades in standing timber 299 

-scale studies 461 

method of conducting 462 

not a check on scaling 118 

tallies, construction of log rules from 78 

talh^, in construction of log rules 58 

Miller log rule 85 

Mine ties 474 

timbers 473 

Miner log rule 35 

Minimum dimensions of merchantable boards, effect on deductions in scaling. ... 107 

size of merchantable logs 99 

Minnesota, statute log rule 73 

Mississippi, statute log rule 68 

Mixed species, yield tables for stands of 408 

stands, effect on yield 393 



542 INDEX 

PAGE 

Mlodjiansky, A. J., method of stem analysis 382 

Moore-Beeman log rule 68 

National forests, log rule 73 

Necessity for board-foot log rules 40 

Need for form classes in volume tables 205 

Neiloid 19 

Nevada, statute log rule 73 

New Brunswick log rule 76 

New Hampshire or Blodgett log rule 30 

Newton's formula 20-21 

Noble and Cooley log rule 35 

Normal density 397 

form factors 212 

yield tables for even-aged stands 395 

use of, by reduction 413 

Northwestern log rule 86 

Number and width of strips, relation 274 

of trees per acre, influence on yields 414 

required for a volume table 155 

Oak, White and Red, log grades 460 

Obsolete log rules 36, 85 

Ocular estimating 256 

estimation of tree dimensions 234 

Old Scribner log rule 73 

Ontario, Doyle rule, over-run 71 

log rule 68 

Orange River log rule 36 

Oregon, statute log rule 73 

Over-run, definition and basis of 46 

deductions from sound scale versus 90 

effect of errors in Doyle rule upon 70 

influences affecting. Methods of manufacture 47 

The log rule itself 47 

-topped tree, definition 158 

Pace, unit of measurement, definition 6 

Pachymeter, Biltmore 248 

Pacific Coast method of estimating 284 

Pacing, use in estimating 262 

Paraboloid, appolonian, definition 19 

Parson's log rule 85 

Partial area estimates 273 

estimates 257 

Partridge cordwood rule 133 

log rule 36 

Peck in cypress 113 

Peeled or sohd-wood contents, volume tables for 176 

Pendulum, or plumb-bob, hypsometers based on the 239 

Penobscot log rule 85 



INDEX 543 

PAGE 

Per cent of area to be estimated, relation to size of area 262 

of total area required in estimating, Table XLIV 292 

scale as a deduction in scaling 107 

of waste in a log, total 55 

Periodic annual growth 315 

growth 315 

of stands 436 

per cent 429 

Permanent sample plots for measurement of current growth 443 

measurement 312 

Personnel, scaling 1 18 

Philippine Islands, log measurement 28 

Piece, as a unit of timber estimating 140 

measure definition 7 

products, converting factors for board feet, Table LXXVI 478 

inspection and measurement 477 

measurement of 466 

volume tables for 191 

PiUng 470 

dimensions. Table LXXV 473 

irregular, effect on solid cubic contents of stacked wood 124 

Pitch seams 112 

Plots, arbitrarily located, use of in estimating 297 

permanent sample, measurement 312 

systematically spaced, in estimating 285 

used in estimating 263 

Plotting, graphic 166 

Plumb-bob, hypsometers based on the 239 

Point of measurement of diameters in volume tables 148 

Pole lagging 474 

ties 474 

Poles and saplings, stand table for 454 

chestnut, specifications 469 

growth of 452 

small 471 

specifications 467 

Portland log rule 35 

Posts, large posts and small poles 471 

Predicting future growth, methods of 320 

yields, application of yield tables in 322 

Prediction of current growth of stands, methods 436 

of growth by projecting past growth of trees into the future 323 

from yield tables, by application of density factor 414 

in even-aged stands, yield tables for 412 

of stands, by growth per cent 432 

Pressler's formula for volume growth per cent 429 

Preston log rule "" 

Principle of the Christian hypsometer 243 

of the frustum form factor 218 

of the Klaussner hypsometer 235 



544 INDEX 

PAGE 

Principles underlying the estimation of standing timber 255 

the study of growth 315 

Prismoidal formula 21 

Products, forms of, into which the contents of trees are converted 11 

made from bolts and billets 14 

volume tables for two or more, combination 193 

Projection of growth by diameter classes 361 

P*urpose and character of growth studies 315 

and derivation of tables for cubic volume of trees 177 

Purposes of study of height growth 365 

Qualities of site, separation in field 448 

volume growth a basis for 385 

Quahty, growth per cent 435 

of site 384 

as affecting height growth 366 

effect on diameter growth 352 

of standing timber, estimating 297 

Quarter girth 25 

or Hoppus log rule 34 

section, definition 6 

Quebec log rule 76 

Record of data on plots, j-ield tables 400 

of timber 276 

Records, scale 98 

Reduced growth of stands after cutting 439 

Reduction in diameter, in scaling defective logs 105 

in length, in scaling defective logs 105 

Reisig method, xylometric, for cordwood 132 

Relation between cubic measure and true board-foot log rules 39 

current and mean annual growth 316 

plots and area covered. Table XLIII 286 

size of area units and per cent of area to be estimated 262 

of cubic and board-foot contents of 16-foot logs. Table III 41 

of diameter of log to per cent of utilization in sawed lumber 40 

Relations of height growth and diameter growth 367 

Relative diameter, in determining growth per cent 430 

utility of different classes of growth data 327 

Re-manufacturcd lumber, grades 456 

Re-plottiiig curves, strip method 173 

Resistance to wind pressure as the determining factor of tree form 208 

Retracing boundaries 267 

Right triangles, in measuring heights 238 

Ruig shake 109 

Riniker's absolute form factor 212 

Ropp's log rule '. 86 

Rot, butt 110 

center 108 

entering from knots 112 



INDEX 546 

PAGE 

Rot, stump 100 

Rough lumber, grades 456 

Roimd products 466 

-edged lumber 14 

Massachusetts log rule for 79 

Rules of thumb, for board-foot contents 252 

for cubic contents 251 

for estimating the contents' of standing trees • 251 

Rimning strip surveys, method of 276 

Saco River log rule 36 

St. Croix log rule 68 

St. Louis Hardwood log nde 35 

Sample plots, permanent, measurement 312 

for measurement of current growth 443 

trees, methods of estimating 310 

Sap, stained ■ 115 

Sapwood, volume 161 

Saplings, growth of 451 

Saw 1-erf, and slabbing, deductions in certain log rules. Table IX 62 

as affecting over-run 48 

conversion of values of a standard rule to apply to different widths of 80 

waste from 53 

Saw kerfs of different widths, corrections for 55 

Sawdust, method of deducting 60 

Sawed lumber, superficial contents 13 

Scale book 99 

caliper • 97 

definition 88 

records 98 

rule 88 

stick 88 

Scaler, legal status 119 

Scalers 118 

Scaling 88 

check 117 

cylinder as the standard of 90 

diameters 92 

from the stump 118 

length of logs, taper as limiting 43 

lengths 91 

of defective logs 105 

practice, based on measurement of diameter at middle of log, or caliper 

scale 97 

practice, based on measurement of diameter at small end of log 91 

in different logging regions. Table XVII 94 

use of cubic foot in 28 

Schiffels' formula, derivation 206 

use in computing volume of tree. 163 

values. Table LXXXI ,,..,.. • , • • 494 



546 INDEX 

PAGE 

Schneider's formula for growth per cent on standing trees 431 

Scribner decimal log rule 73 

C log rule, Table LXXXVI 504 

Scribner log rule 73 

decimal values, Table XII 74 

erroneously termed 68 

extension 74 

Scribner-Doyle log rule 77 

Scribner's log and lumber book 68 

Seams 112 

pitch 112 

Seasoning, effect on volume of stacked wood 123 

Second growth hardwoods, yield table, Central New England, Table LXII 409 

Section, definition, area unit 6 

Sections, measurement of diameter growth on 342 

Sectors, deduction by, for defects 115 

Seedhng, age of 336 

Seedlings, height, western yellow pine, Table L 336 

Selection of trees for measurement in constructing volume tables 154 

Separation of factors of volume, age and area 416 

of site qualities in field 448 

Seventeen Inch log rule 33 

Shade, effect on diameter growth.. 353 

Shake Ill 

Shingle bolts, definition 15 

measurement 122 

Shop grades 457 

Short cord 121 

Shortleaf pine, diameter growth. La., Table LV 362 

Shrinkage 54 

Similar triangles as basis of height measure 235 

Simoney's formula 22 

Site classes and average height of timber 291 

based on height growth for construction of yield table 401 

on yields per acre, for yield tables 406 

use in estimating 292 

classifications, standards based on height of tree at 100 years. Table LX . . 387 

factors, or quality of site 384 

qualities, height growth a basis for 386 

separation in field 448 

volume growth a basis for 385 

Site quality, averaging for entire area 449 

effect on diameter growth 352 

Six classes of averages employed in timber estimating 258 

Size of area units, relation to per cent of area to be estimated 262 

Slabbing and sawdust deductions in 10 log rules, Table IX 62 

waste, distribution, Table VII 56 

Slabs and edgings, waste from 50 

as affecting over-run 48 

deductions by, for defects 114 



INDEX 547 

PAGE 

Slabs, method of deducting 59 

Smalian's formula 20 

use in computing tree volumes 161 

Small poles 471 

Soil map 268 

Solid contents, effect of dimensions of stick on 126 

of irregular piling on 124 

of variation in form of sticks on 125 

of logs, formulae 20 

of stacked cords, measurement 132 

wood 124 

Table XIX 127 

-wood contents, volume tables for 176 

Sound scale, deductions from versus over-run 90 

Southern timber cruisers' method of estimating 283 

yellow pine, grading rules 457 

poles, minimum dimensions, Table LXXI 471 

Spaulding log rule 75 

Species as affecting height growth 365 

effect on diameter growth 351 

Spoke billets, definition 15 

Spruce, Adirondacks, current growth. Table LIV 360 

growth on cut-over lands. Table LXVI 440 

diameter growth of trees, Table LI 345 

in Northeast, on large tracts, method of estimating 287 

Square of Three-fourths log rule 35 

Two-thirds log rule 35 

Squared timbers, log rules for cubic contents of 33 

Squares, definition 14 

Stacked cords, measurement of solid contents 132 

cubic measure, definition 7 

measure as a substitute for cubic measure 121 

or cord measure 121 

wood, solid cubic contents of 124 

Staff compass 277 

Stained sap 115 

Stamps, log 99 

Stand, determining age of 339 

per acre, estimated by eye 260 

table, application in growth studies 421 

for poles and saplings 454 

tables 227 

uniformity of, as affecting methods in estimating 265 

Standard, Adirondack 28 

breast-high form factors 213 

cord 121 

cordwood converting factors 128 

for normal density of stocking 397 

log length in volume tables 182 

of scaling, cylinder as the 90 



548 INDEX 

PAGE 

Standard, Twenty-two Inch 29 

universal, choice of a board-foot log rule for 84 

volume table, form. Table XXX 174 

tables, construction, by curves 174 

definition '. . .' 153 

for cords 177 

for merchantable cubic volume and cords 177 

for total cubic contents, construction of 154 

harmonized curves for, based on diameter 169 

Standardization, need of, in forest measurements 10 

of variables in construction of a log rule 49 

Standards for yield tables 395 

in constructing log rides 49 

of site classification based on height of tree at 100 years. Table LX . 387 

Standing timber, estimating, principles underlying 255 

units of measurement for 139 

trees, measurement 226 

rules of thumb for estimating the contents of 251 

Stands, form of 388 

grown under management, yield tables for 407, 427 

growth of, factors affecting 384 

of mixed species, yield tables for 408 

Stave bolts 15 

Staves, lengths 122 

Stem analysis, limitations of use 326 

of a tree. Table LIX 378 

purpose and application 374 

Stereometric measurement of cordwood 132 

Stillwell's Vade Mecum log rule 36 

Strip estimating, systems in use 282 

method of estimating 273 

of replotting curves 173 

surveys, method of running 276 

Strips, relation of width and number, to area covered. Table XLI 274 

tying in. The base line 281 

used in estimating 263 

width of, factors determining 274 

Stulls 473 

Stump, height of 156 

heights 178 

rot 110 

scaling 118 

tapers. Table LII 350 

Stumpage value, definition. Relation to forest mensuration 3 

of products as affecting accuracy sought in timber esti- 
mating 266 

Substitution of mill factor for log rules in universal tables 146 

of taper tables for tree analysis 382 

Superficial board-feet, correction in per cents for lumber sawed less than one 

inch thick, Table XVI 274 



INDEX 549 

PAGE 

Superficial contents of lumber, correction of log rule for 83 

of sawed lumber 13 

estimates 308 

Suppressed tree, definition . .*. 158 

Suppression, age as affected by 341 

as affecting height growth 366 

Surface checks 115 

defects 115 

Survey, forest, as distinguished from timber estimating 268 

definition 5 

Surveying, forest, as a part of the forest survey 270 

relation to mensuration 5 

Sweep in scaling 116 

waste from 51 

System for timber estimating, choice of 261 

Systems of measurement used in forest mensuration 6 

of strip estimating in use 282 

used in taking measurements of the tree for volume 158 

Tally sheets 277 

unit of measurement, definition 6 

Tape, diameter 229 

Taper as a factor in limiting the scaling length of logs for board-foot contents. . 43 

definition 18 

introduction into log rules 44 

tables 196 

definition and purpose 197 

limitations of 204 

method of constructing 197 

substitution for tree analysis 382 

Tapers, standard, as basis of volume tables 144 

substitution for volume growth 379 

Tatarian log rule 36 

Technique of measuring heights 245 

Tennessee River log rule 35 

Texas, Doyle rule, over-rmi 71 

Third and Fifth log rule 35 

Thomas' Accurate log rule ... 66 

Thurber log rule 68 

Tiemann log rule 67 

Table LXXXIV 500 

comparison with Blodgett rule 42 

reduced to small end diameters, Table LXXXV 502 

Timber appraisal as distinguished from forest survey , 269 

cruisers, training 303 

estimates, accuracy, methods of imjjroving 288 

estimating 9 

choice of system for , 261 

of vmits in MO 

definition 2 



550 INDEX 

PAGE 

Timber estimating, factors determining the methods used in 255 

forest sm-vey as distinguished from 268 

importance of area determination in 267 

limits of accuracy in 301 

methods 267 

six classes of averages employed in 258 

record of 276 

types, map 268 

Top diameters, co-ordination of merchantable heights with 184 

fixed or variable limits 183 

versus variable, influence on frustum form factors 221 

Topographic map 268 

Topography, effect on methods of estimating 265 

Tops, merchantable hmit in 177 

Tor Jonson 207 

Total growth on a large area, factors 447 

height of tree, measurement 156 

increment of a forest includes that of immature stands 443 

or 100 per cent estimates 271 

per cent of waste in a log 55 

versus merchantable contents of logs 16 

heights as a basis for tree classes 184 

yield 315 

Township, definition 6 

Training of timber cruisers 303 

Treatment, effect on growth 391 

of stand, effect on diameter growth 353 

Tree analysis, hmitations of use 326 

measurements required for 289 

purpose and application 374 

substitution of taper tables for 382 

substitution of volume tables for 375 

as a unit in estimating 144 

classes, total versus merchantable heights as a basis for 184 

diameters, measurement 227 

dimensions, ocular estimation of 234 

form, Hoejer's formula for 209 

resistance to wind pressure 208 

record, in connection with volume tables 155 

volume, computation 161 

systems used in taking measurements of 158 

Trees for measurement, selection for volume tables 154 

standing, measurement 226 

Trimming allowance 92 

lengths, in measuring trees for volume 161 

Truncated cone 19 

neiloid 19 

paraboloid ' 19 

Twenty-two Inch standard 29 

Two-thirds log rule 34, 35 



INDEX 551 

PAGE 

Tying in the strips. The base line 281 

Types, forest, use in estimating 288 

method of separating areas of different 290 

use m estimating 292 

Uniformity of stand as affecting methods in estimating 265 

Units of measurement for standing timber 139 

Universal standard, choice of a board-foot log rule for 84 

tables, substitution of mill factor for log rules in 146 

volume table 144 

tables and form classes 215 

Unsound defects, deductions from scale for 105 

Unused log rules 85 

Upper diameters, measurement 247 

Use of correction factors for volume 293 

of cubic rules for board feet, errors in 42 

of diagrams for deductions in scaling 106 

of forest types in estimating 288 

Used length, versus merchantable 178 

Utilization in tops 183 

Valuation survey, forest service standard 282 

Value growth per cent 435 

Vannoy log rule 68 

\'ariable standards, in constructing log rules 50 

Vermont log rule 35 

Volume, age and area, separation of, in yields 416 

and age of stands, relation 449 

and area for age groups based on diameter groups 422 

for two age groups on basis of average age 419 

and diameter of average trees, determining 338 

correction factors for, in estimating 293 

form as a third factor affecting 196 

growth a basis for site qualities 385 

analysis, utility 332 

for single trees, computation 289 

of trees in 374 

per cent, Pressler's formula 429 

of bark 163 

of standing timber, measurement 226 

of tree, computation 161 

system used in taking measurements 158 

table based on mill factors, Table XXVI 147 

data which should accompany 188 

from frustum form factors, construction of 224 

tables, bark as affecting diameter in 150 

based on actual volumes of trees 147 

on standard tapers per log 144 

board-foot, construction 188 

standard or basis 182 



552 INDEX 

PAGE 

Volume, tables, checking the accuracy of 189 

classification of trees by height, in 151 

combination for two or more products 193 

construction, graphic method 169 

conversion from cubic feet to cords 180 

cords, standard 177 

definition 144 

diameter alone versus diameter and height as basis of 152 

for board-feet 182 

for peeled or solid-wood contents 176 

for piece products 191 

for railroad cross ties 191 

graded 193 

ajiplied to tree in estimating 299 

local, construction and use 174 

definition 153 

derivation from standard tables 175 

need for form classes in 205 

point of measurement of diameters in 148 

standard definition 153 

for total cubic contents, construction 154 

for merchantable cubic volume and cords 177 

substitution for tree analysis 375 

universal 144 

Volumes, tree, classification by diameter and height 163 

of frustums, calculation 221 

of trees, actual, volume tables based on 147 

Warner log rule 86 

Waste, definition and measurement 179 

from crook or sweep 51 

from saw kerf 53 

from slabs and edgings 50 

in a log, total per cent of 55 

in manufacture, factor of 13 

in tops and limbs 13 

or cull, effect, mill-scale studies 463 

slabbing and sawdust, distribution. Table VII 56 

Weight as a basis of measuring cubic contents 33 

as a measure of cordwood 137 

Weights per cord for various species. Table LXXXIII 498 

Weise hjqjsometer 240 

Western red cedar poles 469 

minimum dimensions, Table LXX 470 

West Virginia, statute log rule 73 

Wheeler log rule 86 

White cedar poles 467 

relation between circumference and diameter, Table LXVIII 467 

log rule 75 

pine, yield table, Table XLVIII 321 



INDEX 553 

PAGE 

Width of strips, factors determining 274 

single, of bark 161 

Wilcox log rule 86 

Wilson log rule 66 

Wind pressure, resistance of, in tree form 208 

Winkler hj^jsometer 241 

Wisconsin, statute log rule 73 

Worm holes 1 12 

Yale Forest School method of estimating in southern pine 284 

Yellow pine. Southern, grading rules 457 

poplar, in Tennessee, yields of cordwood, Table LXV 426 

Yield of second growth hardwoods in central New England, Table LXII 409 

per acre, spruce, cutting to various diameter hmits, Table XLIX 322 

predictions, accuracy of, factors affecting 412 

table based on crown space, method of construction 424 

construction with site classes based on height growth 401 

on yields per acre 406 

white pine, Table XLVIII 321 

tables, age classes 397 

application in predicting yields 322 

area of plots 397 

based on crown space for many-aged stands 422 

on age, application to cut-over areas 441 

construction 396 

definition and purpose 395 

empirical, use of 413 

example 321 

for stands grown under management 407, 427 

of mixed species 408 

measurements required on each plot 398 

normal, for even-aged stands .■ 395 

record of data on plot ". 400 

rejection of abnormal plots 404 

standards for 395 

use of, in prediction of current growth 436 

total 315 

Yields, definition and purpose of study 320 

density of stocking as affecting 392 

effect of losses versus thinnings upon 324 

of cordwood for yellow poplar in Tennessee, based on crown space. Table 

LXV 426 

Youngiove log rule 86 

Xylometers 132 

Xylometric measurement of cordwood 132 



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